Ideas

[V-Man]

Let's keep autoteam from kicking in until just before the next game starts.

What about autoteam uses 50% time of game to "watch" players and autoteam (switch) after that and score what 50% of game time is up.

50% of game time is a great place to consider. If your suggestion is taken, that could be a good time for the autoteam to kick in, but then it should only hit once -- and only if teams are miserably mismatched.
I believe that autoteam should affect the game as little as possible, and only to be used as a tool that prevents team stacking or persistently unfair teaming.
On the other hand, this could be extremely difficult to prevent as long as some hall-of-famer is playing... :/