Conservation laws are man made, if the underlying universe does not follow them then so be it.

As to other interactions their are a great many possibles but they don't mean much. For example restricting things so only light can move though time does not change the underlying options in terms of information and paradoxes.

PS: Mathematical rigor is again a human idea, our universe could be absolutely random and we would have no way of knowing. At best we can say that seems unlikely.