I do not know if the combination of cardboard and vinyl will fit if you put the vinyl fully around the edges of the cardboard. I have glued vinyl upholstery material to the cardboard and then trimmed the vinyl at the edge of the cardboard. That combination fit easily into the metal trim.

You might want to varnish the back-side and edges of the cardboard (with marine spar varnish) in an attempt to prevent moisture absorption.