I typically take the paper faces off where I'm going to glue as in the fore and aft vertical pieces in the pic below. It takes paint very well, is protected from rot on the faces, etc. The cores are not as nice as marine ply but have almost no voids of any kind. All my edges are epoxy sealed or as in the case of the parts in the pic will have beams epoxied fore and aft on them for cockpit sole supports for this little project. Part of the work you see was done by someone else and I've spent a great deal of time and effort into UNdoing the worst of his work and redoing it with an eye to minimal maintenance and rot protection.
In the end all the areas under the cockpit sole will be epoxy sealed with WEST and their 207 special hardener. I'm thinking to use that hardener as I prefer not to paint the areas in question but be able to see a bit what it looks like over time. However, I'm not sold on that at this moment. I like the brightness of paint in lockers but this area is remote, so to speak, and access will be limited.