IMO, the right way to make it work is to enable closer integration of the two projects. We tried Mono using Wine, and that failed, but Wine has so far not tried using Mono.
How about asking the Mono project to seperate their mono/io-layer Win32 implementation into a shared library, rather than statically linking it as they do in Mono 1.0.2 (ok, maybe be a litle old), then have a Wine implementation of mscoree.dll load libmono.so? Probably not as simple as that, but maybe there's a way forward?
Mike