Thank you all for the suggestions!
I ended up going with the 1x2 backer,

5/8 drywall (what a horrific mess to cut it in 1" and 2" narrow strips),

and regular compound in a tub.


If I had it to do again (or the next time I have to do it), I'll buy the 20-minute or 45-minute mix and mix it myself; I was too nervous and lazy to try mixing my own mud.
Speaking of lazy (or overkill), I wanted to practice using my new DWC 18-4500, so I busted that out for the 7 screws I had to drive. I think I used more screws practicing than I did on the actual project. That's also how I found out that my Recon DWC had the wrong bit holder in the Systainer for use with the Depth Stop Chuck, as it left all screws at least 1/4" proud, even at its deepest setting. I've already submitted that info to the fine folks in Lebanon to rectify...
At the depth I had to fill and with the lower temps in that room, it took the better part of 48 hours to dry all the way through.
First sanding was last night with an ETS125 and CT-MIDI-I, and applied a second coat to level it all out. The STL-450 came in really handy as a raking light (go figure). Although, to be honest, the regular Sys-Lite KAL II does a pretty good job all on its own.
Thanks again, everyone!