Hi, Iggy,
I have always used the craft paints thinned down and finished with a polyurethane spray.
Your present technique seems fine and I agree you should probably finish it with a sealant of some sort.
You can still choose from a satin sheen or gloss.
One other option not mentioned is Kool-Aid. Lots of colors to choose from and simple.
Your puzzles are quite nice.
God Bless! Spirithorse