You have a Tradewind, that's the model name. We have the same bathroom setup and the galley is across from the door.
We left the plywood sub-floor as it was. It has lasted 30 years so far. There were a couple of areas that were soft to the point I could push a screwdiver through them, I removed these and put new pieces in. If you have soft areas that aren't that bad you can use a hardening epoxy. I have no experience of this but it is mentioned a lot on this forum and the Vintage Airstream Mailing List.
The floor we put in floats, that is it isn't fastened anywhere, the weight of the floor keeps it in place, each piece is glued to the previous piece.
The idea of fastening the moulding with double sided foam tape sounds like a great idea. I nailed mine in and as I was doing it I thought of a potential issue. I nailed it at a slight angle from the vertical towards the wall. This ensures I don't nail into the new floor but just miss it and go past it into the sub-floor. The problem I see is now I have reduced the expansion gap between the edge of the new floor and the wall because the nail is in there. I don't think it is a big deal though.
Melvin and Sheila
1972 Trade Wind