That thin cloth-like material is used by the manufacturer to protect the foam while compressing it for packaging. Just like Karen. we used it on the floor to place the foam on while it expanded overnight. The foam topper is easy to lift up when you need to open the counter extension and vice versa. I don't think the topper would fit very well into the storage area under the seats - it's expanding properties would make that it difficult. Ted leaves the small dinette set up as a bed so the topper stays there. He was able to squeeze it into the under seat storage area but it was tough to get in and out so he doesn't bother. Instead of the enclosed topper cover, I bought an inexpensive duvet cover then re-sewed it to fit the topper. I think it looks much nicer. You could store the rest of your bedding under the seats.
I have another topper I roll up and take in my car when I'm going to be meeting up with Ted. That's the only time we use the large dinette for sleeping. I guess it depends on whether you want to leave a bed set up or not. Like I do, you could always roll the foam and leave it in your tow vehicle until you want to set up your bed. I know many people sleep just on the foam seats but I find them uncomfortable. I suppose you could also cut the topper into pieces the same size as the seats - they'd be easier to store but you'd probably want to cover each piece to protect the foam. :-\
You'll have to see what works best for you. It's trial and error. For example, if I'd known beforehand how the seat back cushions sat, I would have done them differently. The curved corners of the trailer don't allow the back cushions to sit flush against the walls. I would have made them in two pieces, one large piece for the back and one small piece for the corner. Then I would have sewn the cover like a hinge so the smaller corner piece would almost bend with the corner. If and when our cushions have to be redone, I will be looking into doing it this way.
