A game using both displays without XSCREEN 4?

I'm trying to make a vertical climbing game, and I want to use both screens for the level as if it were one continuous display. I know I can use XSCREEN 4 to do this, but that creates "dead zones" on the sides of the top screen which I would like to use for a HUD. So, in my effort to work around this limitation using mode 3 instead, I have a character moving from top to bottom seamlessly. My problem now comes from trying to do the same thing with a BG. It not only needs to span across both screens but it also needs to work with BGOFS to move around in case the BGSCREEN is taller than both screen heights combined. I don't want to say this is impossible since I'm pretty new to this, but it seems like it's impossible.

I don't use BG myself, but how does this sound: For the lower screen, program the BG (all except the very top stripe which, when you're at the very top of the game, only appears on the top screen). For the upper screen, program the BG - all except the very bottom stripe. Then, instead of one BGOFS, do DISPLAY 1:BGOFS ...:DISPLAY 0:BGOFS ...

That's clever Square, that way you could use the same BGOFS for both screens!

As I said, I don't use BG, but I believe the top BGOFS coordinate would have to be to the left of the bottom one, so that the seam between top screen and bottom screen matches up.

Text, and GRP commands: GCIRCLE etc..