I'm just wrapping up my boat project.
From past experience, I use the Professional Formica/laminate adhesive for carpet, Vinyl and anything else (This stuff is available for all sorts of applications, I usually purchased it as "vinyl top adhesive" but it's easiest to find at places that make counter tops...it's all the same thing though)
I spray it on with a cheapo paint spray gun from Harbor Freight, Both surfaces, let it dry until you can touch it and it is not sticky. This will allow you to reposition it prior to adhesion. When properly positioned, press it on and rub it out smooth. I use a roller for a good press.
Once stuck, it's stuck forever and virtually nothing effects it. The wood/carpet will fail before the glue.
Best stuff ever and due to my (past) career, I've used them all.
Bad news, as far as I know, it's only available in 5 gallon cans and runs about $110.00 for a can but, I use it for anything and everything I want to stick together.
Look around on carpet, I bought enough carpet to do my entire 16 ft boat (floor, sides and what not) for $44.00. They were Large "outdoor area rugs" from Menards at $11.00 a piece on clearance.
I used 4...I think they were 6x11. FYI, don't get rubber backed carpet.