i don't recall anyone ever fixing the carpet before, I know mine doesn't really move around.
the best I could suggest is that some have built false floors for stereos, etc.
I say have at it and see what you come up with
edit: what your do you have? the pre98 have the "wood" panel attached to the spare tire. in the post 98s the panel is in the carpet ... either way some velcro may help it stay in place ...