The GPD Win certainly seems like an interesting option if you want to stick with windows, but I'm not sure it's as hard as you're making it out to be. The absolutely wonderful
QDrvierStation works great, even on a raspberry pi (or so I'm told). Add a little battery and a battery protector board and you'll be great. You could even 3D print a cute little case and cannibalize an older screen and a joystick for it.
If you have your heart set on windows, I think the GPD might be your best bet in this case. Another member of F4 3D printed side controllers to go around his Suface tablet very similarly to the Razer Edge Pro, but that's quite a janky solution, I would not trust that several hundred device to my own 3D prints, even with my crappy printer. If you use anything other than the default dashboard, including Smart Dashboard or the LabView Dashboard, you will not be able to see that reasonably. The ability to hit the enter button in case of emergency also might be an issue, but you'd just have to get a feel for that. I would guess that the built in joystick would just register as USB internally, but I would ask the manufacturer before hand. Also, I'd hope you can operate all the functions of this yourself, otherwise having another joystick connected to it could be a pain.
Anyway, food for thought, and I think this could turn out well if you consider your options.