You are using comctl32.dll from Win9x which *requires* 16-bit counterpart commctrl.dll. Edit [DllOverrides] in wine.conf and make comctl32.dll=b, or copy commctrl.dll from a win9x distribution.
That was it, thanks. Now it seems there are undocumented stubs in the comctl32 library, IE doesn't even start :(
I got IE working on a standard (well, slightly modified config file) WineHQ build before, but not now for some reason. I don't know what you CodeWeavers guys do to it, but IE seems much happier when on crossover :/