It should be possible to route to the Elastic Cloud using nginx, there's just an extra header you need to supply, eg:
proxy_set_header X-Found-Cluster <cluster-id>;
(note that's the full cluster ID, not just the first 6 digits)
There may be other issues, it's not something I've tried; but based on the error you're currently getting, this extra header should at least get you one step closer!
Alex