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You may have to invent your own method for removing the carpet, don't think I've ever seen that befor!!!
My guess is that the DFO used flooring adhesive. Now you can always go buy lethal mastic removers with good ole methylene chloride, and almighty caustics in them - poisonally, I would research the brand REMOVALL, and there's a KleenStrip remover in a green can. Haven't used either. Don't know what's in them - maybe based on citrus acid. Both say 'environmental' on the label. But better ask them if it's ok to use on old polyester gelcoat. Removers are specific, so it's the right one you want. And ones that won't dissolve your lungs and the meat off yer fingers.
Might pry and scrape a corner up and see if naptha will clean off the residue left on the gelcoat. If it does then look into the "green" removers. Might cross hatch the carpet (what? 2" squares?) with a utility knife to try to get the remover under the turf. Or try BOILING WATER. Or a heat gun, tho it might melt the plastic. You might be able to rent a pole scraper, a kind of longhandled chisel for stand-up work. To avoid naptha for final cleaning, there's a biodegradable cleaner called KRUD KUTTER, that supposedly is very good. GOOD LUCK!