The total run of the stairs cannot exceed 115" because of headroom
issues--the state code requires minimum headroom of 6'8"=80 inches, and
there is a steel beam flange at 115" which is 85" above the floor.

My understanding of the headroom requirement is that it is from the
diagonal connecting the edges of the nosings, and hence part of the
landing at the bottom of the steps has a greater headroom requirement
than 80".

I don't think so: Last I checked, you measured vertically from
the edge of the nosing itself, at least in my ancient BOCA.

I don't understand why this issue is being addressed NOW anyway.
Generally, you figure out how to put the stairs in BEFORE you build
the house. Is this a rehab?
In any case, a floor plan would be helpful, so we could
rule out/suggest things like a raised or depressed landing at one
end or the other, a switchback or L-shaped stairs, or going the other way.

To answer the question you actually asked, the stairs you seem to
have in mind will be perfectly useable, it's just a question of whether
your inspecter will pass them.

--Goedjn