Yes, but that is no different to your blind-signature solution. If your host successfully keeps the messages from the protocol secret, it would be fine. And both (my proof or your protocol messages) don't have to be stored after once used/verified.
Yup agreed. But multisignature works today, and is secure under basically the same assumptions (that one of the two is not evil), and can protect against some additional failure modes e.g. someone steals the offline signer. So thats what I currently strongly recommend.