kingpep,
If you're going to switch pieces for sure, my advice would be to keep the same rim size and shape. I say that because it's what I do. I don't have trouble switching from a deep flugal piece to a shallow piece for big band or pops stuff.
However, it seems to me that once again NE has hit it on the head. None of us know you or have heard or seen you play. We don't know your strengths or weaknesses. Talk to your teacher. If he's so hard to get ahold of, just wait a week or two..........or three.
Marty