Door panel skin question

First post here so bear with me. Awesome site by the way!

I have a door panel insert I’ve been thinking about laying carbon fiber over. The only problem I forsee is the fact it has a ‘soft’ feel to it, meaning I can push it in a little bit. It is a vinyl material. Looking to work on the gray insert in the pictures.

I was thinking I would lay down a tinted black epoxy resin, wait for it to tack up, lay the cf, then coat with a few layers of polyester resin to finish.

I wasn’t sure if putting something that will be rigid in the end will work over something that isn’t rigid.

I would remove the vinyl and thin foam under that, then do the overlay