I would try different solvents in a few different spots. Put down the solvent, cover with plastic for a while so they have time to work, and not evaporate. I've turned a few Porsches into race cars, and the glue they used on 944 carpets is the hardest stuff to get up I have ever come across. The dry ice blast worked, and putting cookie sheets with charcoal under teh car to heat it up worked. SOlvent wise, the stuff that did the best job of anything was xylene. Obviously you have to worry about that being so thin that it may get down into the wood and discolor it, so again, spot clean. See if any of the solvents work well, and again, cover it in sheeting to keep them from evaporating, and you might get it soft enough to scrape up.
Good luck, looks like a mess, but honestly, your quote doesn't seem too bad. Good thing is is a relatively small area.
