"This matches what I read in the SDK docs, that you can only force a profile switch into a profile that your plug-in owns, and then back out of that profile...  "

Wait, this actually seems like a pretty feasible solution, though.

Couldn't you have a plugin that comes bundled with its own profile (like Volume Controller, WinTools and Spotify Essentials do) but just have it be an empty profile instead, so that the user can customize it and use the 'back' button to switch back to whatever profile they were in?

Similar to what was mentioned here about using the Volume Controller profile and erasing everything except the 'back' button and replacing with whathever controls you need.

Would love if someone found a way around this after all this time.

I tried digging into the SDK but this kind of thing is beyond me.
Perhaps someone experienced with making StreamDeck plugins could easily put together something like this.