Double Elim...

When it comes to the end of a double elim single final tourney, the semi-final onwards won't have much impotus to win the games, as you will all be in the same position when you step on court for the final.

Not true, the loser of the winners semi-final can be beaten in the loser's semi-final and would be out. The winner's bracket team always get an easier ride in my opinion.

Here are some other (lame) ways to have a fairer final/process, food for thought:

No change to the time limit on games as the tournament goes on: The loser's bracket path requires the team to play games in quicker and quicker succession and it creates an unfair "fatigue" barrier to victory. Two finals.

If the loser's bracket team hasn't yet played the winner's bracket team then you have a single final, otherwise the winner's bracket team wins by default (double elim challenge).