I have never seen a proposed mechanism of ontological collapse that actually fits this, though.

AFAIK, Penrose's interpretation doesn't describe the details of the collapse process, it just says that above about the "one graviton" level of energy separation collapse will occur.

It doesn't commit to collapse being instantaneous: It could be that the state evolution is governed by a non-linear law that approximates very well the linear Schrödinger equation in the "sub-graviton" regime and has a sharp, but still differentiable phase transition when approaching the "super-graviton" regime.

The GRW interpretation assumes instantaneous collapse, IIUC, but it would be a trivial modification to have fast, differentiable collapse.

My point is that non-differentiable collapse is not a requirement of objective collapse interpretations.

The inability to send a signal that you want, getting instead a Born-Rule-based pure random signal, doesn't change that this Born-Rule-based pure random signal is, under ontological collapse distributed FTL.

But that's an issue of QM, irrespective of the particular interpretation. Indeed the "spooky action at distance" bugged Einstein and many people of his time, but the modern view is that as long as you don't have causal influences (that is, information transmission) propagating FTL, you don't violate special relativity.