you know- it wasn`t so much the resonance that it changed as it changed the tuning a little sour- I just couldn`t get the drum to sound right until I took it off the mount- I had to put it back on that day but it certainly led me to believe I wouldn`t use rims mounts myself. It could have been a fluke or just my ears?
Could also be that the RIMS mount was bent, meaning it was putting tension on the tension rods. I played on a suspended tom that just didn't sound good, and it turned out that this was the problem--the mount was pulling outwards on the tension rods. The tom should be freely-moving while attached to the mount. When you first buy a mount, you need to bend it a little so that it takes the shape of the drum and lines up the holes perfectly to the tension rods (I had a drum store employee show me this...he was absolutely right).
Also, do you tune by feel? If so, a RIMS mount would diminish your ability to do that, and maybe you just tuned it sourly as a result...??? If you tune your toms in "jazz/bop range", RIMS don't do much to increase the sustain, but then again, neither do the heads at that point...