I would paint it with an oil based primer and then oil based enamel. Primer is the magic sauce that makes paint stick.? No primer, no stick.

I'd also paint the plywood sheets before you install them, so you get the areas that will be covered after install.? Then a final coat after you screw on the reinforcements over the joints.

Don't put the rubberized paint on bare wood.? I don't think it will stick.? I just got done peeling some silicone rubber caulk off bare wood in my fridge compartment.? It was really easy because the silicone rubber didn't stick at all to the bare wood.