Have you looked at QUIC? It seems like it addresses the problems with HTTP2 over TCP as well as providing some additional benefits like like speeding up the secure connection establishment.
Yes, I'm aware of it, though not as in-depth as I'd like to. AFAIK, it was a bit unfinished yet eg. not having any congestion control story, which is very important. But yeah... it's what what HTTP2 probably should have been in the first place.
