Ideally, the series should end at the Freeza Arc and any attempt to continue it should be no more than an epilogue of sorts. Assuming I can't change the Freeza Arc's ending, I'd have Vegeta head out into space after the tension surrounding having him on Earth amongst all the Z-Warriors gets too much and his desire to find Goku acts as the final straw. In doing so, he runs into King Cold, who was on the way to heading for Earth to find the man who killed his son. This is not for revenge, however, but to offer him the role as ruler of the empire. Vegeta says Kakarotto would never accept, but he might take the job if he can get the last remnant of Freeza's legacy out of the way. They fight, but Cold is too strong for him (about equal to the Freeza FP Base Goku fought in this continuity) and takes him prisoner. Vegeta is given no choice but to serve the Cold Empire once again as they head to Earth.
Meanwhile on Earth, Pilaf has created more boxes that block the signal of the Dragon Radar so he can attempt to gather the Dragon Balls again. His desire this time is to use them to go back in time to when he had the Dragon Team imprisoned and kill Goku and Oolong when he had the chance. He manages to perform this successfully, with him going back and using his Pilaf Machine to kill all the group and let his past self get his wish of ruling the world. This continues for many years until Raditz arrives to wipe out all life on Earth, though Pilaf reveals to him the existence of the Dragon Balls and secures his life by saying he's a descendent of the Dragon God and only he can summon Shenron. Raditz lets him live and brings him and the Dragon Balls back to Freeza's main base. The other Pilaf is still alive due to having used the Dragon Balls for eternal youth and in wanting to get on Freeza's good side, reveals he is from an Earth where Raditz never did any known damage and life still goes on as usual. Curious about this, Freeza decides to leave eternal life on the backburner and instead wish to be able to visit Pilaf's timeline with all of his empire, including his father. Here we still have time travel acting as the basis of the arc, but in a far more consistent, less convoluted and less convenient way.
In space, Goku has been tracking Cold for a while after sensing a Ki similar to Freeza's and starts heading towards Earth. As for Freeza's group, he is shocked to learn the Dragon Balls would've scattered and deactivated and, thus, kills the Pilafs out of rage. His timeline's Vegeta reveals he's heard stories about the Namekians' wish granting orbs and chooses to head to Namek once Freeza has dealt with seeing how his empire is. He enters his main base of operations to find his father there with Vegeta at his side, the main timline Cold revealing all that has happened. He then kills the Vegeta of Freeza's timeline, saying having a weaker Vegeta who already held the seeds of rebellion would be a worthless addition and only make things more complicated. Not wishing to be killed again, Freeza transforms into his true form and decides to go to Earth and destroy it from space.
As he's about to do so, however, a blast clashes with it and Freeza had barely enough time to dodge it. Though most of the crew of his ship escaped fine, the blast still had enough power and enough of a direct hit to kill his timeline's Cold and damage the ship. Freeza and Cold then descend to Earth normally, whilst Ginyu pilots the ship.
Down on Earth, Goku is revealed to have fired the Kamehameha. Not knowing how Freeza survived but knowing of the stakes well, Piccolo decides it's finally time to fuse with Kami. As all of Freeza's forces descend to Earth, the Z-Warriors (minus Piccolo) stand to fight them, with Goku challenging Freeza directly. Freeza recognises the look of Bardock and is enraged a Saiyan could kill him. Goku attempts to settle things quickly by going into Super Saiyan, but struggles to do so. The time he spent away from Earth was to better control the form, yet he didn't have the rage he had in the battle against Freeza to activate it at will and has learned that with a boost surpassing that of Kaioken by far, the strain it puts on his heart is overwhelming once he has finished battling. It's then revealed through a flashback that after escaping in Ginyu's pod, the fatigue hit him all at once and he would've died from cardiac arrest had the people of Yardrat not helped him. Instead, he's forced to fight using Kaioken x10, though Freeza quickly goes into 50% and starts trouncing him. In that time, Piccolo fuses with Kami and arrives on the battlefield, though even with his new power and Goku using Kaioken x20, they're only able to keep Freeza from using any more than 70% whilst Goku's stamina eventually begins to drop.
As for the other battles going on, the humans and Gohan easily deal with Freeza's men, Gohan personally killing Dodoria, Zarbon and Cui when remembering what the former did to Dende's village whilst the humans face the Ginyu Tokusentai as in filler, beating them in much the same way. As Cold is prepared to step up to bring a swift end to this, Vegeta strikes him with a surprise attack, saying he'll put an end to the one who let Freeza continue his evil acts in the first place. Fuelled by desperation and Saiyan pride, Vegeta manages to break his limits and match Cold in battle, though the strain is evident on Vegeta. Eventually, the two kill each other in battle. Raditz and Nappa watch on, inspired by their prince's bravery and how even these lowly humans are standing up to Freeza better than they can. They use the opportunity to escape the battle. Meanwhile, Ginyu has yet to make a move, hiding back.
Goku eventually summons enough rage to become a Super Saiyan and before he can allow Freeza to power up, he kills him. Despite this, the battle isn't over as Ginyu uses the body change to steal Goku's body and kills the real Goku, before starting battle against the Z-Warriors - the body of the Super Saiyan Goku who was their defender having become their greatest threat. Though far weaker than SSJ Goku would be, Ginyu's adrenaline and desire to destroy all enemies of Freeza allows him to maintain the form. Knowing what has happened to his father, Gohan snaps and is filled with enough rage to charge forth and fight on par with this Ginyu with Piccolo there to help. Still, they are only able to keep up against such a strong opponent for so long and a fatigued Piccolo sees resorting to the Mafuba as the only option left. In classic Dragon Ball fashion, however, it fails and Piccolo dies, the rage Gohan feels being enough for him to fight on par with Ginyu himself. Eventually, Ginyu's confidence in his abilities starts to waver and his stamina decreases, with a solid punch from an enraged Gohan being enough to revert Goku Ginyu back to base. The pressure it puts on his heart is so much it instantly bursts and Goku's body lies dead.
With the battle over, Raditz and Nappa show up to plead for mercy and say they've been inspired to throw away the past and try and build a new future for the Saiyans on Earth. With them not being a threat anymore, everyone agrees to let Raditz stay, though Ten, Chaozu and Gohan are quite reluctant on Nappa staying until he says he has no idea who they are and Gohan pieces together these two are from an alternate timeline. Kaio then gives them co-ordinates for New Namek and they attempt to revive Goku and Piccolo. Goku, however, can't be revived due to his soul having died in Ginyu's body and due to Ginyu's power, switching them is beyond Porunga's power. They then consider reviving Goku in Ginyu's body, but Goku tells them the same thing he did in the Cell Arc and departs. Despite this loss, everyone returns to Earth.
Five years later, major changes have happened. Piccolo has assumed the position of Earth's Kami, though decides to use his power to actively stop any injustices he sees. Gohan has managed to balance studying and training to continue the path of Goku's successor. Yamcha and Bulma have married and had a child whilst Ten has started the Shin Tsuru Sennin-ryu school and Kuririn the Shin Kame Sennin-ryu school. Raditz and Nappa have adjusted to Earth life, Raditz helping the Son family whilst starting a family of his own and Nappa making a career out of cultivating Saibaimen and bringing them from a race of fodder soldiers to a useful work force for humanity, becoming a celebrity for his "invention".
We then skip to ten years later, in which Gohan has published his book Groundbreaking Science to bring Ki control to the masses. When talking to Kuririn, the human thanks him for having made the Kame school popular enough he can support his family (let's say his wife Lazuli and daughter Marron) before Gohan heads to the Heavenly Realm to see Piccolo. He asks Piccolo if he still hasn't restored the Dragon Balls, to which Piccolo says even if he trained to harness Kami's Dragon Clan abilities, it's better that way as to not incite essentially another Freeza's ambitions, viewing them as a greater danger than a saviour in a parallel of the 23rd TB's ending. Gohan then says he plans to write a new book so they will still exist in the hearts of others, telling him the title will be "The Legend of the Dragon Balls and Son Goku."
We then skip forward 100 years and the Tenkaichi Budokai is taking place. Two young men of the Kame and Tsuru schools face off, one a descendent of the Son family. An aged Piccolo watches from the crowd, remarking how even long after Goku and Gohan have died, their legacy remains strong.
We then skip 1,000 years after Goku's death, in which civilisation has changed so much due to Capsules becoming more advanced and opening up a truly futuristic environment, along with almost everyone being so attuned to Ki that cars are gone completely and everyone uses bukujutsu to travel. In a school, we see a teacher telling the class about Son Goku, now one of the most important historical figures in human history. In a temple, we see a group revering him as God incarnate and that the battle against Freeza was an apocalyptic showdown that ushered in paradise on Earth. In a university, a class debates on how much accuracy should be placed into the accounts written by Gohan due to bias. In a smaller country, we see someone cursing the allies of Son Goku in ruining the world as we see the use of Ki and Saibaimen have lead to far more advanced warfare. We see the many differing perspectives of the Z-Warriors in the public eye long after their deaths.
Finally, we journey into the future a million years later. By this time, humanity has gone through so many changes due to warfare that technology has gone through rises and falls and despite Ki users still being standard, none of humanity has a clear picture of when Ki became a standard for humans and each culture has a different story of who lead them into the age. On a visit to a mountain, a man (let's call him Toriyama) finds a strange device lying between the rocks and presses down on it, a somewhat damaged book being preserved inside, though the cover is damaged, two words are still visible - Dragon Ball.
We then close out with this line by the narrator - "Though ages will come and go, the story and legacy of those bound to the Dragon Balls lives on."
prior to their fight in Mamiya's village just to add a little more motivation to Kenshiro's rematch with Kaioh. 
