I didn't want to wade through 19 pages of text and I know this has been answered before, but why would it be a bad idea to integrate this into the P2P network on a bilateral basis? Wouldn't it still help a bit?
See
https://github.com/TheBlueMatt/bips/blob/master/bip-TODO.mediawiki for something similar which is more targeted at the P2P nature of Bitcoin. See-also
https://github.com/TheBlueMatt/bitcoin/tree/udp-wip for something which is intended to eventually replace the Relay Network - a whitelisted-peers-only secondary relay channel that is easy for miners to use between their own nodes (ie its just an additional flag) and will also be much faster than the relay network today in its worst-case (and probably average) relay times.