Figured this out, so for posterity:
You have to install a third party codec that will treat each MIDI channel as a separate control surface. I nabbed this one: https://koshdukaimusicreason.blogspot.c ... emote.html
Set up each channel as a control surface in the preferences menu. They're under the <other> manufacturer. While you're there, disable the actual control surface or you'll continue to get spam from all channels on the selected sequencer lane, and make sure none of the virtual surfaces are selected as the master, or else you won't be able to lock it to an instrument.
In the rack, use the right-click menu to lock the virtual surfaces to the appropriate instruments. Then make sure all your desired sequencer lanes are record enabled and go!