I think it will be better to fully disable early data for people without full control of DC's network equipment. I don't know why Cloudflare made a decision about using headers and Too Early response. They have full control of their POPs. It will be better to measure RTT and use UDP based KV storage with tickets only for clients with high RTT. So for clients with RTT higher then access to KV storage it will be better to issue tickets, for other clients it will be better to drop early data and use full handshake. Currently, I'm working on a project with the same idea.
To measure RTT you need to perform a round trip. Hence the name. But the _whole point_ of this feature is to avoid incurring the cost of an extra round trip if possible.
There is no need to send extra data to measure RTT. On the TCP handshake SYN/ACK you already know RTT. Linux kernel provides this info in tcp_info data structure.