is that you can really see what you got. Your description is really good but seeing it makes things a lot easier. With the additional info you just added, I would suggest that you keep popping the tiles off and look at getting a Wonder Bar or other small pry bar with a thin blade. When you are down to the adhesive, go with an adhesive remover to get the black gunk.
You can sometimes use that sander for a small amount of removal and the big drums are better at this than the new lightweight disk sanders geared to homeowners. 40 grit paper can take off a lot but how much is too much to make this economical is a tougher decision. That's really why I suggested you have someone else look critically at the situation.
The other thing you may have to consider is nails sticking out of the floor or very shallow. These can tear up the sandpaper real quickly. They should be buried, but a lot of things "should be" but aren't.