Mine had no tack strip like residential, but did have thousands of staples, they must get paid by the staple. You should be able to just pull the carpet up & then pull the staples that didn't stay in the carpet.
Your problem is the way these things are built, the floor is 1st, including carpet & tile/linoleum, then everything including the exterior walls are built on top of the floor.
Unfortunately water is the worst enemy of a rv, usually once you've found the leak source it's already done the damage.
I had an old 5er with water damage & ended up laying new 1/2" plywood over what was left of the old after removing as much damage as possible.
Hopefully someone has better suggestions for you!
Danny & Linda
Former '13 Redwood FB owner