Paraphonic: you could try the modmatrix random on osc levels and other parameters. Not exactly, not repeating, but not dissimilar.
For duophonic: use both layers in monophonic mode, have one layer low note priority the other high note priority. Whenever you edit the envelopes and LFOs, be sure to edit both layers at the same time to improve the illusion.
Polyrhythmic/sequenced: Another thing that may help is modulating the amount of one pulse LFO by another, in differing amounts or directions/polarities. If you are happy with a set speed - i.e. not clock synced - you can also work some magic by key-syncing LFOs and setting different phases. It's not a polyrhythmic patch, but you could take a look at Jeanny's Genius bank 4, patch 98 (dual layer).
For on/off per keypress and quantisation effects, I'm just as curious as you to hear a solution. Hm, you could be very crude and use three LFOs with the 50%, 33% and 25%, in sync, but phase shifted modulating the same destination. You'd at least get 0, 50% amount, 33% amount, 25% amount and then down again. Such things, however, need some careful planning in advance or long-winded trial and error.
HTH, best wishes, Jeanette