Seems to me that if you are using marine grade ply already, one would prefer to choose to paint with a good oil based paint. I know there are pre-painted sign blanks, but sounds as if someone went on the cheap and got the unprimed ones. The real ones are coated with a paint similar to OneShot.
I know it's probably too late and not really relavant to the OP at this point. But I've not offered a "Wood Based Sign" in over 10 years. When there are products out there like DiBond, Alumalite etc... No priming the edges, no warpage, products carry a warranty, unlike wood. Perfectly smooth surfaces, signs, vinyl, prints etc. always look their best. Throw on some fancy edge cap, and call it a day.