Probably the fastest, easiest and cheapest way to sand the paint off a floor is not by calling a hardwood flooring contractor, but by phoning any of the companies listed under Janitorial Equipment & Supplies in your yellow pages phone directory.
That's because you can sand that paint off, but, if whom ever put that paint on knew anything about paint, he would have put on an oil based paint (actually an "alkyd" paint) which would stand up much better to foot traffic than a latex paint. And, alkyd paints are chemically very similar to the polyurethanes commonly used as hardwood floor finishes or "varnish". In fact, the polyurethanes sold as varnish or hardwood floor finishes are also called "urethane modified alkyds" in technical literature to differentiate them from other kinds of polyurethanes, such as moisture cure polyurethanes.
And, every janitorial service company will have a floor machine, and the sell sanding disks that fit on floor machines specifically for sanding the polyurethane off of large gymnasium floors. So, any janitorial service company that sands the polyurethane off of a gymnasium floor will have the equipment and people experienced in this work to sand any kind of paint off your floor.
And, a janitorial service company generally charges less per hours work than a hardwood flooring contractor.
Go to
CENTAUR Floor Machines Limited
and click on the Floor Machines link
The "Woodpecker" floor machine is an ordinary floor machine connected to a vaccuum cleaner...
Or, just phone around to the places listed under Janitorial Equipment & Supplies in your area and find out who sells "sanding screens" for floor machines. That place will know who buys them, and whomever buys them is almost certainly in the business of sanding floors with a floor machine in preparation for refinishing.
Home Depot rents floor machines, and if you buy a 120 grit sanding screen and a high productivity pad to hold the sanding screen in place, you could do most of the work yourself.
On the following web page, the small diamond disks are for hand grinders to polish marble and granite floors and counter tops, whereas the large 17 and 20 inch sanding screens are for use with a floor machine:
Janitorial Supplies - Sanding Screens
The price of $50 to $90 for a 17 to 20 inch sanding screen is almost certainly for a box of 10. Where I buy my sanding screen, they sell them individually for about 7 or 8 dollars each.