I wonder if it's feasible to reference the TLS/SSL session against the session cookie? While the HTTPS session itself is probably transient, you can tell something is up if the same session cookie is being used with two different HTTPS keys.
As far as I know, it's not supported by any current browser (I welcome feedback to the contrary) but is included in SChannel. Given that we've only recently (arguably) gotten away from SSLv3, I don't have high hopes that it will be viable to require channel binding in the very near term.
$_REQUEST["salted_SHA_hash_of_symmetric_TLS_key"]
You'd save the current key to a DB, and manually check it in future requests.