Sounds like most of the confusion could be solved by both of you:
1) only saying "got it" when you really have it, and you are in better position to play the ball than your partner could or would be.
and 2) believing your partner when they say "got it," not telling them "no you don't, I do!" mid-point, and not taking yourself out of position for the next ball just to possibly cover in case they don't actually "got it" when they said they did.
2 would likely follow pretty easily if 1 can be achieved first. Of course 1 is easier said than done in the middle of a point, but still from your description it honestly doesn't sound like either of you do that very well and to me that sounds like the root of the problem.
I'd also add that, in the case of an overhead, the person who could have the overhead should make the call, either "got it" or the opposite. I don't think the partner who would have to cross behind should be making a call at all, but rather reacting to whatever the partner says, either trusting that they "got it" when they say they do, or going to get it as soon as they indicate that they don't.
Last edited by dcdoorknob; 12-15-2012 at 02:47 PM.