Covering exposed insulation paper face
Flame-retardant polyethylene (6 mil, I think) is commonly used. You'd sort of end up with a double vapor barrier, but since they're tight together it's probably not a problem. It's readily available at building materials suppliers.

Regarding your "ridiculous codes" comment, walls of highly-flammable paper are a genuine safety concern. It ignites much more readily than the paper on the face of drywall, for example, and spreads flame very quickly. Surely you prefer that the occupants have a fighting chance at survival, and those downward-trending lines don't happen by accident.