I'm going to attach part of a journalctl log of the hang/crash.
This is an Arch Linux host using the regular 'linux' Arch Linux kernel (version
4.7), Mesa 12.0.1, and Wine 1.9.17 (no matter if I use -staging or
-gaming-nine) with a Sapphire R9 280X 3GB GDDR5 OC DUAL-X GPU.

A video of the crash as it happens:
http://nanosector.ddns.net:9090/BGLL0XLY/file_309.mp4
Note that I don't know how long that video will be up for.

I've tried mesa-git to see if that eliminates the issue, but it behaves in the
same manner.