I was thinking about how I would do something like this with my modest gear. I don't think I would automate everything, rather I would do the following on my Bass Station II: do the quick modulations with pitch LFO assigned to aftertouch. Direction doesn't really count because of the speed, any waveshape and direction could work. Then do the slow stuff and big changes with pitch bend.
If we want to be more exact we're emulating banging on a tremolo arm on a guitar to modulate harmonics, so the LFO would be a saw with some slew with negative depth to pitch.
