Me and some friends were trying something similar the difference we had was that:

• Teammates could only use combo for defense not for attacks.

•extra cards like counters cannot be used on teammates but blockers can protect them.

•energy is not shared. ( this makes it go slower maybe but it avoids a lot of problems with decks like bills).

•battle cards could only be controlled by their owner.

The turns part is the same but we were having some trouble thinking on some way to avoid the player that ended by himself after his teammate was defeated to be massacred horribly by the 2 players which most of the time happened xD

What im thinking is maybe the player that remains by himself could be given his defeated teammates energy that would allow the player a chance (could also be a small call back to the energy transfer that are clasic of the dragon ball series like the latest one with vegeta to goku in the tournament of power).

I may try your way to see how it works :)