Teardrops n Tiny Travel Trailers

My lack of progress gives me lot's of time to think..here's a question. I think my 5 ft. wide interior will have plenty of wood showing, and was thinking carpet on the floor and up the sides a bit, and using auto foam backed headliner over a 1/8 birch ply ceiling. The foam backing on the headliner is 1/4 inch. Here's site that has the material I was thinking about...lots of colors:

Headliner supplier

Anyway, when I built the framing, I left a 1/4 inch gap between the solid outside and the ceiling sill to place the birch ply.






Here is the question...will the 1/8 ply backer mounted with 1/4 foam backed headliner have enough give that I can slide it into a 1/4 inch slot for a friction fit? Not married at all to this...just looking for alternatives.

You'd rather have headliner material showing than the nice birch?

I myself would have to use the headliner because I'd screw UP the birch and would need it for a fix, but in your case?