I had the same problem with the Mic-Eze clips. Rims mounts are a cool concept but it does compromise useing clip on mics.
I think your only options are to:
A) mount the toms in such a way that the bulk of the Rims mount is on the side of the drum (rather than the top of the drum)
B) Mount the Rims mount on the bottom lugs of the toms (rather than the tops) I read about a drummer who did that - an added benefit would be that you can change the top head without messin' with the Rims mount - the down side is it would add height to your kit
C) Use the long LP claw, that mounts to the bottom rim
D) USe standard mic booms
E) Use tape - although if you have to use tape - use masking tape rather than duct tape - it's easier to get off.