Glidden porch paint will stand up to what you are looking to do, bed sheet will give a smoother finish than canvas, the marine paint could give a good gloss finish, but, I would test the adhesion to Glidden paint first, especially as this board will see a lot of flexing in the waves.
I love the idea, I boogie board often, never thought of making my own. I did find the boards we bought last year are made with a beadboard foam core with nicer foam glued over it. The adhesive they used failed, I re glued the skins on with gorrilla glue, they survived another day in the surf just fine.
Since you mentioned my foam boats I'll share my latest boat not foam, but with foam bulkheads and deck clamps, and my first boat that isn't a box
https://www.facebook.com/media/set/?set ... 212&type=3