"Here, treating the expected population of zebras as literally P(zebra)=0"

That phrase lacks a finite verb.

I don't see that inferential statistical methods break down. On the contrary, they give exactly the correct answer that one would expect. The variance under the null is zero, so the z value is infinity, so the p value is zero. Whether you do a z-test, a t-test, or a Poisson test, you're going to get p = 0, and therefore reject the null. Your trying to link this to the claim that 0 is not a probability is begging the question.