That’s terrible that you lost the screen already. Hopefully the warranty process is painless.
My one suggestion would be to use the Director software running on another computer. That computer could even have a touchscreen and be located next to the surface. You can switch the main UI screen with the Director software.
I think A&H doesn’t want to switch the UI between the surface’s two screens due to the physical buttons located next to the screen. They are not the same on both screens, so switching the UI to a screen without the appropriate buttons would be pretty frustrating.