I don't know the crypto side of things-- is it possible to create a half-key which can be combined with another half-key? So for example, the webserver can customize half the key per transaction (leading to unique addresses for the customer), but not have the information to spend that tx until its half-key is combined with the locked-up-safe master-half-key...
Yup.
Secret sharing. Really easy math wise as well...it's just a system of linear equations IIRC.