Formaldehyde in melamine is likely more of an issue than the remaining phenol in kiln dried heated pine. What is the particles in the substrate of melamine? pine, fir, spruce, aspen, tropical hardwoods? who knows I don't. There is at least as more issues with melamine than pine. Out gassing is increased by higher temps and high humidity ref, Healthy Home and Healthy Office By Richard Kanuka-Fuchs.
DO NOT USE marine varnishes (specifically SPAR varnish) it is not made to harden but stay soft and flexible (spar = mast, booms and yards) that move a lot. It always out gasses as it never hardens fully. Regular exterior varnish will be fine.
there are a lot of coatings available from horribly expensive to in expensive. Predictably the best are expensive and worst cheap. The toughest are two part epoxy or LP paints. They are hard to work with and costly (LP is over 100$ a quart) if you have never used them it might not be the best time to start.
Regular polyurethane is likely the best cost and durability wise. I like colors in plastic by varathane. Just make sure it has a good long curing time (7 days+) Latex paints can be used they are just not as hard wearing products. AFM safe coat makes a product called hard seal that is hard tough and seals the wood product from out gassing. (plywood has some urea formaldehyde as well but a lot less as the glue lines are much smaller) It might be a product to look into as a final coating.
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