I also agree, with my reasoning being assuming you're using a heat gun (or anything meant to reach the same levels of heat) those are actually made specifically for paint stripping. So I'd worry about all your paint melting or flaking off if you painted it first then heated it to shape it. Maybe that's not an issue with foam but just something I've been thinking about as I've been working on my own foam armor.
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Shy Gal (Nintendo Fan Design)