When you try to open the project in Windows, exactly what happens? I just manually renamed a Windows project’s .scrivx file, and the project opened just fine. (Native Windows, not WINE, but it shouldn’t matter.)
Two suggestions: have you tried the Linux version of Scrivener on your Linux install, instead of the Windows version on Wine? Since you have Scrivener on the Mac, and it is the most advanced of the bunch, I’d assume you’d want to use the full suite of compile, etc. tools there? I run both, and find that the Linux version is about 95% perfect for everything I want to do in writing, sorting, composing, etc. I don’t believe you’ll run into the name-change glitch that way.
The other suggestion is to ensure you’re running the latest version of Wine? There’s a thread here in the forum for getting & compiling Wine, since most distro sources tend to be pretty far back on versions. It’s fairly simple, but the machine will run for so long you’ll want to go watch a movie or something. Just sayin’ …
One thing to check, open up the project file on your linux box. Are there files of 0KB that mirror hte correct files/documents? Delete the 0KB ones. I had an issue with that, but it’s fixed. i haven’t had any compatibility problems. Are you using at least Scrivener 2.0 on Mac?