> One option I've seen previously is transmitting a hash of the password, then hashing + salting it once more, which relies on avalanche effect as you suggest.

If the client-side hash is fixed, this is no more secure than transmitting the plaintext password, since as far as the server is concerned, it is the password. You could, however, send a nonce to the client, send back H(nonce++password), calculate H(random++Hsent), and compare that to H(random++H(nonce++password)) calculated on the server.

> talk to an actual cryptographer

I am not your lawyer^Wcryptographer and this is not legal^Wcryptographic advice.