Have you thought about spoofing the EDNS to (a less truncated version of) the nearest Cloudflare edge node's IP? This would be no more of a privacy leak than traffic from your edge to origin servers, while providing generally enough geographic information to keep latency low on the source. This is at the very least compliant with the spirit of the RFC, no?
EDIT: another comment, though somewhat hearsay, suggests that Cloudflare's caching could make this difficult to implement: >>36971650