It may be time for GitHub to build out multiple availability data centers and use BGP as an anycast tool. We do this. I have public facing IPv4 space that is announced from multiple facilities. Having an IP address hosted from multiple facilities is a powerful tool. This allows providers to hit our datacenter through the least amount of ASN routes. We original did this to minimize latency and create faster regional transaction processing. As an added benefit - DDoS traffic also gets routed to the nearest facility "load balancing" a DDoS so that it only affects a single facility or it splits up the 10gbps of traffic among many facilities if it is coming from many sources. O'Reilly's BGP book has a great chapter on "Anycast."
From the sounds of it their architecture may not support this. If they had a SAN solution capable of replication to multiple data centers like HP LeftHand's product or a multiple master DRBD configuration they may be able to host github from multiple active datacenters and announce the block equally so that providers route traffic to them because their ASN is closest.
Thanks for the book recommendation. Is that the one by Iljitsch van Beijnum?
Other than the added complexity, can you share any details about the cost? It seems like theoretically some managed hosting providers could offer this assuming they were in multiple datacenters, but I haven't seen any that do.