What I've learned about EVA finishing and how I intend to proceed once I start using it, barring new contradictory information:
Smoothing foam faces: brief passes with a heat gun. It'll become shiny as the cells close.
Smoothing foam joints: 1) make good joints, slowly closed with BARGE contact cement. 2) silicone caulk with blended acrylic paint of the foam's colour (probably black). A few drops of paint should be sufficient, in theory.
Sealing foam for paint: Plasti-Dip or Rustoleum underbody spray both work and retain flexibility. Underbody spray is way cheaper in the US. If you have a good size compressor, balloon latex is better value and also retains flexibility, though latex based products do age.
Priming foam for paint: unnecessary, unless you're using enamel, then building up a flawless finish to apply gloss to is preferable. Rustoleum Stops Rust primer should be fine over the sealant and wet sands nicely.
Hardening foam: rigidity requires a rigid material, so you'll need a coating resin. Lots of resins are designed for smooth coating. Smooth-On Epsilon is the usual standard, though pure epoxy resin - sometimes sold as tabletop epoxy- works just as well. Hardening is very messy though, since you have to let it drip off the sides for a full coat with no meniscus. There are other options for resins too. Smooth-On 65D functions similarly thanks to its slow cure time for rotocasting. Other companies make the same products under different names and may be cheaper, though resin systems are generally somewhat expensive across the board.