Update: the operation was a success, for both joy-cons! I've taken the guts from an official joy-con, the shell from a bootleg, and a brand new battery. No drift so far, too. And yeah, the right joy-con had way more crammed inside; you'd think they'd put the ir chip and the nfc chip on opposite sides, but nope.
I recently replaced the sticks on mine with those magnetic ones that aren't supposed to drift, and despite the left joycon being more simple, it was also harder. They pass an unrelated ribbon cable over the back of the stick that you have to remove.
Now that you've done it once, I can recommend the gulikit hall effect joystick kit, which is a drop in replacement. I've done it for my kids' joycons and it shouldn't ever need fixing.
I also installed a replacement antenna for one of them, you can buy a square one that fits where the original goes. And for the other side where the antenna is etched into the board, there's a handy pad where you can solder on a wire. I used a 6.25cm long wire, stripped and soldered at the middle, this makes a dipole antenna tuned for 2.4GHz, and just tucked it inside the case.
Since doing this the signal never drops out. It used to be nearly useless for sitting on the couch, now it's a solid connection.