I posted an alternative construction elsewhere in the thread.

The thread model is an adversary that gets unlimited access to the values stored for this purpose, and knows the function used to compute it. He wants to check if a given email is in the set. One-way functions is provably the best way to be able to ask yes/no to the question if this email is in the set with no false answers. I have not said anything about using computationally expensive one-way functions because that does not matter if the function takes 10 seconds to compute. He already knows what emails he wants to check.