Doesn't the fact that it doesn't have stamina issues imply they can power up without getting the huge strain though? Vegeta's statement may imply this is the case:
Vegeta: “They’ve judged that state as the best! If they get used to that as a matter of habit, then even if they raise their battle power, the strain on their body is very small! [ ] They’ve thought this through…”
Like, if SSJ has 75 of stamina and powering up (Grade II/III) reduces it to 60, but once MSSJ is mastered the stamina is 100 and once you power up (Grade IV) the stamina is like 80.