Are you sure that the plastic layer is not a laminate, and came from the factory bonded to the wood underneath? If so, I would suspect that that wood is plywood
, and might not have a very nice finish-able surface.
If this is the case, and you can get the surface of the laminate defect-free, you could "simply" laminate a new layer of veneer, or your choosing, over the plastic.
PS - Simply is in quotes above because I have never done this, and I have no idea how easy it would be for you to do on your boat!