Late in the process I realized I had not accounted for the thickness of the sheetrock that will need to be applied to the living room side of the alcove to close it off. Thankfully, the realization came before I installed the studs and I ripped them on the table saw to allow for sheetrock when we get to that stage (another, later project). I installed the studs on either side of the opening, directly to the existing finished framing, with 3 1/2" screws. I'll remove the trim around the opening when I start the next phase.