Midi would be fantastic, maybe overkill though.
The simplest possible way of syncing to hardware would be to have a "step advance" triggered by the joystick fire button. I have a hardware sequencer that can provide this kind of signal (Arturia beatstep pro)
I'm not sure how this would work with the internals of miniseq though. Are "note lengths" calculated from the tempo, or are they fixed?
I occasionally take part in modular jam sessions and this would be a great thing to take along.
It's the nicest c64 music thing I've seen so far, and there are some really fantastic things around these days.