Just got it to boot consistently on the OLED:
I ran the controller layout tool when launching the game & set vsync off.
Then, I set compatability to GE Proton 8-25.
Booted right to the game after that.
For a few other tests:
I went back to the controller option and set vsync back to on, and it still booted without a problem.
Rolling back to the default proton version just gave the white screen again.
I cleared out all the FF12 compat data so it would reset the proton setup, then skipped the controller stuff (vsync still on) and set proton GE 8-25, it booted without a problem again. Maybe it’s just the proton version that needs setting.
Yup, you can reset that under the game settings/properties at the bottom of the “general” page, under launch options.