I think I've seen this before.
If what you have on your floor resembles blobs of stuff that might drop off the underside of your car's engine, then that's decomposing black foam rubber chips from what's left of your underpad. When they made black foam rubber back then, it wasn't very stable and gradually decomposed, but I don't know why.
If the wording "a black greasy kind of muck" accurately describes what you're dealing with, the best thing I've ever found to remove it is a strong mixture of laundry detergent in water. Just add two cups of laundry detergent to a gallon of hot water and clean it off the hardwood.
I found that soap solution to be a lot more effective than anything else, including paint thinner, because the stuff on the floor isn't oil or grease. Also, it takes time to break down that black stuff, so work different areas at the same time. Get the area to your left wet with the soap solution, scrub the area in front of you with a nylon bristle brush, and be mopping up the area to your right with a sponge, and just keep rotating that way, giving the soap solution time to work.