Tread separation and blowing the skin off a tire is likely not due to the tire rubbing occasionally over bumps. I've wore holes through a plywood trailer floor and didn't lose any tires. I've had multiple tires, 5 or 6 in 3 sets that would peel like an orange and they lived a shelters life in the garage under my boat.....all Goodyear Marathins.
Just fixed a trailer this am that one of the crews was hauling a mini exc around on that was so tongue high that the back tandems were rubbing on the frame. It's pretty common.
Buy some good tires and you'll be good. Suspension issue depends on how much/ hard they're hitting the trailer. I'd want to get that thing jacked up a bit or buy some smaller tires if you can.