I achieved to make the Arduino Mega and the Axoloti to speak to each other through UART in a few minutes (through a 3v3 <-> 5V level adapter
I think that MIDI is a good solution.
Instead of inventing my own obscure protocol, i can use MIDI.
MIDI with sysex can be an elegant solution to synth parametrization (much like the good old synth editors).
The main difference with the previous synths is that each patch is a new synth, with different parametrizations.
Basically, the arduino+screen is a dedicated MIDI controller.
Thus, we can imagine a protocol where the Axoloti sends a Sysex to the controller to inform it which parameters are available and how they should be presented (layout) and controlled (Sysex, CC...).
After this phase, the controller (Arduino + screen + pots... or a tablet through MIDI bluetooth...) adapts itself and controls the Axoloti as the Axoloti told it.