I put a FDP32 socket-370 heatsink on my Tbird socket A with no problem. Of course this doesn't mean that it's ok to do, and I probably just got lucky and didn't bust my core.
I just had a bright idea, why can't you just bend the clip a little bit to give you less resistance? (I assume that is the problem, as the clips fit the same) You should be able to bend it enough to give you enough less resistance (bad english, I know). Also, you could just use a copper shim/spacer.