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My floor was squishy in about half of the TT. Supporting from below was not an option due to holding tanks and other items in the way. I did not want to remove the couch and dinette for this project either.
I opted to reinforce from above and embrace the difference between the 2 areas instead of trying to disguise it. I used a completely different floor material and made the transition in a logical place.
I used 3/4" OSB to reinforce the floor. I am very happy with the results, I can only assume another $30.00 for Oak plywood might have been better, but this is fine.
I did not glue down (All you would be gluing to is the vinyl) just used 2-1/2: deck screws (countersunk).
I opted for lots of commercial grade 2 way tape versus carpet adhesive. If this fails to hold up I will glue down. The carpet is actually a 6' x 8' area rug from WalMart for $20.00. Had enough left over for a new "entrance" rug.
Total cost for project around $75.00, took approximately 6 hours.