I charge $3.40/ft. to sand with dust pickup machinery and apply 3 coats of oil poly. For a standard stain I add $0.30.ft. If you have a small area or it's really cut up I'd add something more, plus add for whatever surface protection you might need. Those prices sound quite high. 2-1/4" Red Oak costs less than $3.00 here (wholesale) and that's higher than you should pay in the northeast.

I have used Goof-off to clean up spots, but a large area will need special treatment. Perhaps you could soak a rag in it and lay it on the spot, but then yuu would have t he vapor contaminating the air in your house. Maybe you could carefully use a razor blade scraper or large chisel to scrape most of it off.

Hardwood throughout my entire first floor, including the kitchen and all entry areas. Residents don't wear shoes in the house. Human residents, nor furry ones. :) Visitors are not given any rules upon arrival. :) Most people see you walking around in bare feet, or socks, or slippers, and immediately move to take off their shoes. Depending upon who they are and why they are there, I often tell them don't bother. For instance, if it's the HVAC guy and he's going to work in the cellar, I couldn't care less if he keeps his shoes on. As someone noted upthread, the nice thing about hardwood is that it does clean up very easily. I prefer the residents keep shoes off the floor b/c it does keep the floors cleaner, but there is no way I would ever make a guest remove their shoes. As far as damage - most of the damage to my floor comes from the toenails of the 20 pound furry lunatics who share my home. Yes I keep them short - no lectures on appropriate dog nail procedures please! They are young and love to run and play - nails dig in on cornering no matter how short they are. :) However there has been some damage from people in shoes who had rocks stuck in the treads. Most of it from the early days when the house was under construction because sadly my GC was an inconsiderate moron regarding things like this. TL:DR. It's hardwood. It dents. I do what I can to keep the dents to a minimum but don't stay up at night about it either.

It is entirely possible a buff and coat (using the original people with the original finish) will deal with this....at the painter's expense of course. Go ahead and bring the refinishers back to ask the question, "Can a buff/coat deal with what we have here?" There answer will be the one you take back to the paint company. As an estimate, a buff and coat costs "roughly" $3/sf (depending on your local market conditions for employment, etc).