And on the latex paint .. if you paint the top and bottom facings, use Flat or maybe a Satin .. not gloss, or semigloss. Flat has a much higher silica content. The flatter the paint, the more silica. The glossier, the more latex. Wouldn't really matter on the sides, but I' still prefer flat or satin because it will allow the styrofoam to "breathe" a tiny bit.
Otherwise, cycles of varying heat and humidity will cause the latex surfaces to weld and the paint will turn into glue. Dusting with talc after drying could be another option, or addition. I would use PermaWhite Satin plus talc, but only because I already have both.
I would have opted for wax coating the inside, but that would be a whole lot more trouble than paint, and I've been paranoid of doing the wrong things, using chemicals, etc. .. If Michael Bush says paint is ok on the inside, that's good enough for me. ... Unless there's a detail that hasn't been mentioned : If the boxes have already been waxed on the inside .. then, don't paint over the wax. It will turn into a mess