My nephew bought an old firehouse. Based on its age (>100 years old), I am pretty sure the second floor was originally hardwood. Sometime after WW-II, the hardwood was cover with (likely) asbestos based tile using black, asbestos "cutback" adhesive. This is a very large area, >2000 sq ft.

Please don't bother warning me about the dangers of asbestos in these materials. Appropriate personal protection and disposal WILL be used.

I have removed this type of tile and adhesive on a small concrete floor. Very labor intensive. Even after 2 applications of the removal solution AND etching of the concrete, there was still some staining on the bare floor. I don't believe that this can be sanded without quickly clogging sanding belts.

How can this hardwood be saved ?

Most floor finishers that I know will not use a belt machine to remove cut-back.
It never dries so sanding abrasion melts it and sticks to everything where it touches the machine from the wheels to the sanding bag or dust control unit.
It's a real mess, but I have heard that it's possible to use stove oil to keep it from clogging up sand paper.
Once all the old tile have been removed, including chips that will adhere when sweeping up, the job is all yours.
You would be better off laying a new floor over the old asphalt tile.
There are products that help dissolve the cut-back so it can be scraped up and after the cut-back is removed a floor sander could clean it up with a coarse paper,16 grit would be a good start.

Are you a professional ?

I am being told, even with most of the cutback removed, professionals will not touch such a job because sanding puts too much dist in the air and some of that will likely contain asbestos.

Diamabrush makes a product to do that on hardwood. www.diamabrush.com

You are on your own when there is asbestos in your home, unless you hire a professional asbestos removal company. A homeowner may work on the project without special licenses. In the past I have removed cutback from a vertical grain fir floor to save it for a client. I have sanded this stuff a couple of times in the last 35 years.

What solvent did you use if any ?

Did you use plain sandpaper or did you use something like a Diamabrush ?

I scraped the surface to clean the floor as best as we could, removing the surface coating. Then we used 16 grit paper, open coat. I have an older American 12 sander that did the job taking the rest off.
Since then I have seen that there is a cut-back remover that dissolves the tar.
The diamabrush would probably tear the softwood floor to shreds. It may work with some of the very old floors if they have never been sanded before because the old flooring was a full one inch thick, back then. As the flooring gets thinner with sanding it will deflect more between the floor joists, creating more possible problems.

Knowgood luck