I bored out a hole in the 3rd floor for the 2nd-story stairwell, by overlaying the 2nd floor (which has the same perimeter size) and tracing the stairwell hole onto the 3rd floor. Then I cut out the stairwell hole piece from the 3rd floor with the Dremel using a thin sanding wheel piece (which I discovered does a decent job of this when I was bashing the last spring fling build). I primed, sanded down, and then glued the main pieces together, laying the house on a side to try to weigh down some gaps:

Some folks prime after gluing together, but I have been using Kilz water-based primer which seems to raise the grain and needs some good hard sanding, which is much easier to do with an unassembled piece, so I have been priming first.

Then I duplicated the 1st-story stair support pieces by tracing them onto 3/32" basswood. I cut strips from 1/8" basswood for the treads and risers, using the existing pieces as a guide. I used thinner basswood for the stair supports because although basswood is a soft wood, it does get tough to cut alot of it with an exacto knife.

After all the pieces were stained, I assembled the supports with treads and risers and put the structures in place to dry so that hopefully there won't be too many gaps when I go to install them for real.

Here is the 2nd story staircase assembly, where I used the original staircase pieces; I'll use the back pieces from the kit also to close up the staircase.

Here you can kind of see how I was maintaining the right spacing by using spacer sticks cut from popcycle sticks. It helps keep the staircase together and square.

Here you can see the 1st story staircase assembly, where I used the new pieces made from basswood. I am going to close in the understair all the way to the floor and put a closet.