So here I'm basically trying to describe what changes you would make to the way JWT validation is currently done. IIRC, the JWT goes over in the headers. I'm suggesting adding 2 headers - one with the base64 of the json of the JWT, the other header is the ecdsa signature of that.
This way, you know whoever it is that logged in and provided their signed public key, has to be sending this request because they signed it with the same key - which is locked to _this_ browser.