Comment by LorenPechtel

Blocking said search indexes is probably a good thing.

I'm thinking perhaps a system where you feed it a credential, a small program runs and maintains a pool of tokens that has some reasonably finite lifespan. The server that issues the tokens restricts the number of uses of the credential. Timing attacks are impossible because your token requests are normally not associated with your uses of the tokens.

And when you use a token the site gives back a session key, further access just replays the session key (so long as it's HTTPS the key is encrypted, hard to do a replay attack) up to whatever time and rate limits the website permits.