There is not a single dictionary that lists "заец".
You mentioned the case of кофе as an analogy. Well, I should argue that it's not, really. All the words in Russian that end in е are neutral, except for coffee. So, logically, it should be neutral as well, it's just that we have traditionally used it as masculine and its usage as neutral hits the ear wrong with no linguistic or logical reason whatsoever, only historical reasons.
The spelling заец, on the other hand, is completely illogical. Consider the plural - зайцы. The я->й shift is common in Russian, however, е->й is not. So, there would be no compelling reason to accept this weird spelling.