Got it working again. Running the alpha version Steam Runtime 3.0 (sniper). Mouse works. Hand controllers work. It's a bit choppy when I pan my head side to side, but it's tolerable.
I removed the Compatibility mode. Steam installs 4.0 by default, so I didn't see a reason for backleveling that. The mouse is quite choppy. Hand controllers work fine. There's a bit of screen tearing, but with the headset at 120hz, and graphics set to 120fps under the vsync section, it's reduced.
I switched back to public release (no beta or alpha), and I unchecked force compatibility. The hand controllers are the best option for the cockpit. There's just a little screen tearing as I pan my head, but it's very tolerable.
I would be happy to help with testing on Linux.