There is a "normal" popup mattress and a thicker premium one. From what I have seen the FR HW units have the much thicker, premium one.
I have the thinner version and hated it. I put a 3 inch thick king foam mattress topper on it that came with a 1 inch thick fabric mattress pad included. I had to cut down one side I think about a foot to match the king end, put a mattress protector around it and am really happy with that.
You with the premium mattress I would think would be even happier.
I believe it was this one:
https://www.samsclub.com/p/serta-4-i...=plp_product_1
It is a bit of effort. With your HW you may be able to fold it up and put it on floor for travel. I have to get the bunks in, there is about a 16-18 inch space between them. I pull the mattress back to cover both the front and rear bunk so there is space for the tent at the end otherwise closing is a hassle.
Before doing something like this, assuming you don't want to put it on the floor I would suggest seeing what kind of room you have above your bunk mattress and the roof.