I gave up on this plan after getting two rows’ worth of LEDs hooked up. Negotiating the forest of jumper wires was even harder than I expected, and on top of that the sockets kept coming loose from the LEDs’ skinny little leads.
However, at this point I figured out a way to use the Teensy’s PWM ports to control RGB LEDs. If I forgo the TRRS jacks and solder the wires connecting the two keyboard halves directly, I can have more than four conductors.
I’ll still need to figure out the right resistors for the LEDs, but with the Teensy controlling the LEDs I won’t have to fine-tune the brightness in advance. I can just choose a reasonable minimum resistance and turn down the brightness with software.