Alright, last night I got my ass in gear and finished framing the main closet wall. I was quite happy with myself!
I decided to add the fire wall (same as the other original walls in the house), but I'm not sure if I should bother with the bottom row. In the other original walls, there's a second row of studs that follow along the height of the baseboards (I'm assuming since this makes it much easier to install solid wood mouldings, which sometimes need to be bent slightly to fit nicely). But I don't really need it here. I have additional studs because of where I put the door, and I have plenty of solid.
This is one of the original walls on the main floor for comparison:
Next I'll need to build the "box" for the built-in, frame that in place, and re-run my electrical (into the new wall).