Wouldn't such interactions create feedback loops that would, in turn, create a cascading generation of neutrinos?

I didn't look at the data, but the point in time the detection cuts off is also relevant - it should match the time it took the first neutrinos to arrive at the detector. If some of the original neutrinos interacted with something outside normal spacetime and that made new neutrinos appear closer to the detector, some of the original neutrinos should have arrived at the detector at the predicted time.

Anyway, this is a very interesting concept. Hope you can somehow test it.