I do love a build thread. Thanks for posting. I would use new wood and try some other stuff like foam where you can. The main point is that it needs to be fixed and it's not a huge trailer, so the weight you're adding is not a big deal unless you get excessive and somehow overload the axles.
That being said, one of the previous posters was right in that you shouldn't build it with wood like a deck with 2x4, 2x6, etc. The support is in the metal frame, and you will most likely be fine with thinner pieces and plywood.
When I built the cab over bed in my class C I looked at what they had used originally and I replicated it with some possible improvements. Mine turned out very strong. You could add a few lengthwise supports to fix any poorly designed flooring. Keep in mind that part of sagging is the difference between new and old material. They build it and it holds up because it's new which means it's underdesigned.
I cut styrofoam into my walls and filled any gaps with "great stuff". That would be a cheap and lightweight solution for airgaps, but really you should be concerned about water not air.