The new setup will have a very strong clip, about double the clamping force of the SocketA spec, so I don't think you'd want to use it even if you could. The heatsink's clip has a bolt at each end which bolts down into a metal spider that's mounted to the underside of the motherboard to distribute the stress.
The only heatsink I've seen so far that has any supposed cross-compatibility between present CPUs and the Athlon 64's is the
Zalman CNPS7000-Cu or its hybrid aluminum/copper sibling... and that's cross-compatible between Pentium4 and Athlon 64, but not SocketA.