Doesn't Docker with with VMs on Windows and Mac? (At least I know it does on the Mac).
Maybe it's still possible to mount an X11 socket from Windows/Mac to the VM (and then to Docker?)??
It's still trickery, but if you can get that to work on the Mac and Windows Docker clients, then you could distribute the Linux version of the custom apps and everyone is happy :)
Not fragile at all. Just mount the appropriate socket and there you go.
Alernatively, you can also run vnc or rdp inside the container:
https://gist.github.com/gmacario/11385611