Here's the last part of the staircase build. Once I can afford to cap it in the finished wood, I'll be making more posts about it, but for now, it's "done".
To secure the three "floating" ends of the stringers at the top step, I custom made 3 metal brackets. These are made from 1/8" mild steel (7$ from any hardware store). I cut the length into 3 sections, marked them, and drilled them. They were bent roughly to shape with a vise and hammer.
I could maybe have tried some sort of "joist hanger" hardware on these, but the 1/8" steel will be much stronger than the thin metal versions. Making these myself was probably cheaper as well. They are secured directly to the structural beam.
After I had the top secured (in the correct spot for my measurements) I then nailed the staircase to the walls on either side. I used large 4" nails for this.
This morning I cut and installed all the rough steps (nine 3" screws each, and also secured on the revers with 4 screws in the risers).
This shows the 4 horizontal screws on the back sides.
I'll also point out that I put all the "nice sides" on the back part of the staircase, since I probably won't finish the back. This is why the front part of the stairs already look especially cruddy (paint drips, scuff marks, etc).
For the top step, I simply installed a 2x4 filler block at the top, and made a taller riser. The riser is then screwed on the front, and on the back.
The top "step" (floor edge) will need special detailing/moulding work, and it's basically going to get a 3 sided rim (painted the floor colour), and hollow columns on the ends to continue the illusion of the door frame down to the step. A bit hard to explain, but you'll see this in detail when I eventually put it together.