Flat paint will retain some of the HF absorption characteristics of the foam. Gloss will make them pretty reflective for a brighter top octave. Eggshell seems to be the best compromise. It sounds open, but not bright. Two coats sprayed with an airless or rolled with a small foam roller works very well.
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Dave,
I'd like to try some of these but still am not clear on the paint options

. In terms of absorption, it just seems the thickness/depth/hardness of coating would make more difference than whether it is shiny. In my case I would need a bit of absorption, so maybe 2 coats of flat make sense. So if you want to pay for pre-paint, you just tell Greg whether you want flat, eggshell, or gloss and he lets her rip with 2 coats? The sealer is double the money, so what are the advantages of doing that vs what you described above?
If I wanted to paint it myself, is the mini-roller method a pain to do? Unfortunately, I don't have a sprayer.
Could you do a progressive set of coats to see the effect, knowing there you can't then go backwards. i.e. start with the most absorption (flat), then add coats to make it more reflective? Is there a point of too much paint on it?
Sorry, I be dense

Tom