Interesting, but why not use the timestamp baked into response headers? There's also domain.tld/cdn-cgi/trace for cloudflare. I don't know how cloudflare will take using that page for this though.
Access-Control-Allow-Origin: * (or site origin), and Cache-Control: no-store
Also, watch for mixed content (HTTPS page trying to fetch HTTP gateway), either serve the probe from the gateway or expose /time over HTTPS.