Just another look at this problem...
If the flooring was down for some time and it was the old
petroleum/solvent based adhesive (which it sure sounds like) you may be
in trouble. The petroleum stain has no doubt over the years has seeped
deeply into the wood, >especially< in an open faced wood like oak.
The reason this is a problem is that the foot traffic is concentrated
into a small pathway on the stairs, which constantly grinds in the
ahesive every single time the stairs are used. If by using the term
"scored" you are referencing wear, no doubt the original adhesive
(which can take years to lose all of its solvent) can work its way into
those scored areas making the pentration of the stain very deep.
When I have run across your problem, we do a test tread for the client,
and time the guy doing the prep to see how long it should take. If it
takes more than a couple of hours a tread and riser, my clients have
always bailed out. We scrape first, then add a little acetone, then
scrape some more with a cabinet scraper. When we have everything off
we can get with the scraper, we sand starting at 80 grit with an ROS,
and work up the grits. Corners and edges are done with a 1/4 sheet
The last one I did, we painted the treads a soft earthtone, and I came
up with the idea of cutting an oak door skin into strips and tacking
them onto the risers. That way we didn't lose the oak look on the
stair case. Standing in front of the stairs you saw the pretty new oak
risers, and that gave the owners enough to make them happy. The risers
were stained and finished to match the rails and balusters, and after
it was finished it actually looked great.