A few questions and suggestions:
Why do you have your GiffinGrip on a bat? I have mine adhered directly to my wheel head and it clips on nice and tight.
Have you tried dismantling it, bringing it back to the factory set up and re-assembling it? Maybe that's why there's some wiggle?
You've had it a year, has it always done this?
I noticed that with mine if I tried to trim when my pieces were just a hair too soft, I would get squeamish about tightening the pieces all the way to avoid warping the piece near the rim. But once I recognized the problem and waited until they were a little harder, I found I could tighten it very strongly and it would hold the piece just fine. There are also some different holder pieces, some that come with the GiffenGrip and some you can buy extra that are made for different shapes and made to be able to move closer to the center of the wheel if you need to trim narrower pieces. Also the ones with poles, that hold a piece higher up. Hope any of this helps. Good luck. Maybe try calling/emailing Giffen Grip directly? I had an issue a while ago and they were very helpful over email.
K