That might be a bit convoluted, but only once
Something to consider. I might just put a good 5" memory foam topper in that existing cover and a light mattress cover over that (to get rid of the scratchy feeling of the upholstery).
I don't have a full bed at the other end, with the SL, but I will likely get a roll-up foam pad that I can tuck away in that upper cabinet (that isn't big enough for much anyway) for the trips that I have my friend riding shot-gun. Gives that sofa a bit more of a comfortable sleeping surface, eliminates the crack somewhat at least.
I'll bring over a thick comforter as a test "topper" & check out the clearances next time i'm over at the TM (she's in a storage yard here in town - easier than trying to park her in my front yard, and actually better for her - she won't be parked under a 50' pine!). I figure I can set up my video camera inside as I try to close her up. Give me a really good idea of what kind of space I have to work with in there.