This is an interesting question... more broadly, how fast could the GPIO pins be driven?
Im assuming the 3kHz rate, is just quoted, as the control rate... but presumably this could be exceeded in the same way as audio is, i.e. you write to a buffer that is N bytes, giving you 3xN kHz.
so then the question is,
a) whats the limit from the STM32F4?
b) is there a way to get chibios to read this buffer, and write to the pins at a guaranteed rate?
I guess (b) is the problem area...
(a) could be found in the STM ref quite, (b) in the chibios documentation , though I guess @johannes already knows the answers
theres a few areas, Id like to go look at...
go check the current audio code, is it the responsibility of the codec to guarantee the timing of 16 byte buffer?) , how would things like usb audio, or audio via X3 work (I2S?) ... how do/would they reliably clock?
if this is controllable, then again, writing the gpio pins would seem possible in a similar way.
(and are easier(?) since your not caring about syncing any clocks, you just want steady timing)
as for the problem space...
if your using mono, can't you use the other channel as an data channel?
(unfortunately the headphone socket is hardwired to the audio output iirc, and the additional aux channel too)
on the other side, many signals on axoloti are control rate, so reporting at higher rates wont buy you anything, but I'm assuming your talking about audio rate signals.