This might be stupid to bring up, but these days I'm mostly playing classic games on my laptop, when I'm on the go. Incidentally, my laptop has GNU/Linux as its operating system installed, and so I use both SteamOS+Linux Steam and Win32 Steam. I use WINE as a compatibility layer to get Win32 Steam and certain games running, and even played FFVII with the New Threat difficulty mod installed.
When I try to install Reunion, it is mostly successful, but it gets stuck on the final steps (I can't recall at the moment, something like "sorting files"). I left it at these steps for about an hour, and the entire time it used CPU cycles and appeared to be working. I assumed it may have been file permissions, so I made sure to chmod the FFVII directory to 0777. It appears to be patching minigames when it gets held up, killing some of these processes moves it forward (I know that's a bad idea, but I was experimenting), but it never fully completes.
I know you probably don't intend to support the patch working through WINE, but just in case your interested, I thought I'd bring it up. I can run the patch on a fresh copy of FFVII via terminal and paste the logs for you if you are interested.