More stepping through the code, comparing Windbg to gdb, and I found another landmine. Shrinker gets the address of the NTDLL procedure LdrAccessResource, and looks for this code:
FF74XXXX push [esp+X] E8XXXXXXXX call ....
Instead, it finds an unimplemented procedure in Wine. So now I will look at LdrAccessResource (and friends) to see what's involved in implementing it, whatever it is.
--Rob