I apologize for failing to keep up with this thread! I completely agree with Joe about bracing the bottom back of the stair unit. My lapse in judgement.

I also agree about using 2x4s instead of 1x4. My initial reason for using 1x was to minimize weight as much as possible. These days, I keep running 2x4s through my table saw to rip them down to approximate 1x4 size for framing flats. They end up costing a little more than a dollar apiece, instead of close to five for an actual 1x4. Tricky work, but it can be done.

The stair units that I am building will be a little different than in my drawing now. They will only be 24" across, and will be made completely from 3/4" plywood. I have cut full size pieces for the facing of each step, as well as a full length back to the stair unit. I will also rip down 2x4s to 2x2s, to make railings for the stair units.