A couple things come to mind, Honch.  You alluded to the resonance.  Some designs 'cap' feedback well before runaway oscillation.  But sometimes that sweet spot is teetering right on the edge.  Another thing is the 'attack'.  I added some fast attack/short decay to my RandomFilters preset, and it makes all of the difference.  You may be able to do the same thing with a ramp (inverse sawtooth) LFO over the amplitude.

All in theory right now, but I'm thinking primary modulation speed & secondary LFO rate set the same.  Primary modulation waveform shape at Sample & Hold; secondary mod source at Ramp.  High resonance and just the right Phaser variation can't hurt.  (I'll have to try some of this when I get home.)

Now, back to the great "dirt debate" …