The best incremental refinement is short-lived certificates auto-issued by intermediate CAs. [...] The refinement being pushed instead of the obvious one is "OSCP stapling"
An OCSP response is a short-term statement issued by the CA that a TLS server's certificate is still valid. It can be thought of as exactly the sort of "short-lived certificate" that you describe. Stapling allows a TLS server to cache this response and present it alongside the main certificate. If only the TLS server contacts the CA to get OCSP responses, the CA can't see clients.
From a footnote in the proposal: "In the current draft, there are additional requirements, including that an OCSP check for the CA certificate is successful".