When we do stair wells (without the 2x4s attached to the stringers and wall - this is probably the key point), we place strapping to prop the first sheet section up, cut also to overlay the floor joists (as you stated, to avoid the ugly seam), then stack from there. We use a level to make sure that the first sheet is level. The stacking allows exact measurements for the angle. We do both sides, then install the ceiling last.Sorry to disagree WB. I always start at the top for stairs. Be sure to take at least 6" off the first sheet so a joint does not break where the bottom plate/ floor joists / top plate for the next floor all come together. (Often something doesn't quite line up and makes for a bad joint.) If you start at the bottom, you're starting off with an angle that would be, at the least, time consuming to determine. The stair stringers have a 2"x4" between them and the wall running at the same angle as the stringer (a spacer for drywall and skirt board) fastened to the wall. No way to stack the rock off the floor. I've done it "top down" for 30+ years. It could be done, but not likely by a "production" drywall hanger.