I started putting up some drywall over the newly rebuilt "corner #1" (of 2) next to the archway. I also started adding casings to the archway (I can't wait to reinstall the salvaged old one, and blend/putty everything to match.
I only did half, really, and I won't be able to install the top until I mud the corner joint. The only casing I put in place is the left and right centre "columns" (side pieces), which aren't in the way of anything else.
I also disassembled, fixed, and reconnected all the screwed-up duct work in "corner #2". Everything is now straight, uncrumpled, and all the joints are taped (except the one I couldn't reach, which is at the end of the run (right before the floor vent).