As part of finishing my basement I'll need to rebuild these stairs to account for the higher floor level. The back of this stair case is currently open to the lower basement, but that will be getting closed off. I think I understand the basics of stair construction, but I'm wondering if there's anything wrong with extending the subfloor (3/4" OSB over 1" XPS) all the way under these stairs to have a continuous thermal/moisture barrier? Would it be better to stop the subfloor at the base of the stairs so that the stringers are supported directly by the slab?
Practically speaking, it will be better to keep the integrity of the new floor intact. But the small unsealed gap will probably not be a major concern if you leave them on the slab. I do have to say, however, a difference of 1 3/4" on the bottom riser does not meet current IRC code. The difference in riser height cannot exceed 3/8 inch. You may be grandfathered since the stairs already exist however. The only way to be compliant is to recut all the stringers adjusting the riser heights to stay within 3/8" max difference at any riser.
Tearing out and rebuilding stair seems like a lot of work. I was trying to think of a way around that...and it's actually an idea I've done before when building a deck. The off-the-shelf stringers had to be cut to handle the distance from the deck to the ground. Obviously this screwed up the bottom most riser distance. What we did is shimmed each tread a different amount to adjust them all to have the same riser distance.
So, for example, let's say you have 10 stairs. You've taken away 1.75" from the bottom most riser.
1.75"/10 = .175"
So, on the top most stair, you'd add .175" of material.
On the second top most stair, you'd add 2 * .175 = .35" of material.
And repeat all they way to the bottom most stair = 10 * .175 = 1.75" of material.
In the end, you've basically adjusted the riser of each step proportionally to make up the 1.75" that was taken away.
Granted, that may be a lot of work too, though should be easy to do if you happened to have a bench planer (maybe an excuse to get a bench planer!?)
Even without a planer, you might be able to 'round' each shim size to the closest dimensional lumber. So, .175 = 1/4" ply. .35" = 3/8" ply, etc.
So did that answer your question? Probably not. I guess I'm thinking it's best to have the stringers in contact with the slab, and since the current ones already do that, it'd be nice to not have to tear out the entire structure and replace.