From a comment on the linked post:

"Both Google DNS and OpenDNS implement the (Google-proposed) ecdn-client-subnet DNS extension, that basically forwards the higher part of the client IP to the authoritative DNS for the specific purpose of latency-based routing...

I assume you're not using latency-based routing for static data (otherwise a CDN would solve it). In that case, you're out of luck because it looks like Route 53 doesn't support ecdn-client-subnet"