Consider using P2P HTTP/2 #227
Description
A few years ago a Peer-to-peer Extension to HTTP/2 was proposed at the IETF. I believe gRPC is often deployed internally, where playing with new features like this is possible.
It may be worth considering there, if this allows optimizations to your protocol, that would make it worth while to try this out and give feedback to the Author.
I wrote up some thoughts on interesting implications it has here for relative URLs.