Right, last night I FINALLY figured out how to use a bluetooth joypad under RetroArch, with the buttons in the right places, and without killing the built-in controller on the #gameDad.
I'll do a full write-up for https://gamedad.club later in the week, but as for the general gist, there's a bug in RetroArch where saving a controller profile associates your bindings with the wrong bit of hardware, so when you exit and reload, it loads the bindings for the Bluetooth controller onto the inbuilt controller, breaking both.
RetroArch has a database of controllers that it can, in theory, automatically set up properly; in practice, they're guesses, Clippy for your controller. To fix this problem, I had to erase all the guesses (KILL CLIPPY) and write my own .cfg files.
Sounds hard but honestly that was super easy, it worked pretty much just like 90's MAME or whatever, just press each button to get its code then copy it into the file, the part that took three nights of fiddling was figuring out that Controller Clippy was the problem.