As a side channel dns over https still works even with tls to google.com and then putting Host: dns.google.com into the header. Frequent updates to applications and push notifications can be used as side channels too. You can also register a bunch of domain names ahead of time using hash of a current day, month, year and then let the app generate domains names to query on the fly and query them over normal dns. The censor would need to reverse engineer the app to figure out the domain generation algorithm.
To make proxies hard to enumerate you can shard the mapping of ids/phone_numbers to proxies in a such way, that each id receives multiple proxies using multiple different sharding schemes. This not only makes it harder to enumerate, but also lowers the chances of someone else obtaining the same set of proxies as the censor and rendering the app unusable. Changing IPs then forces the censor to chase you, but never really catch you to censor the app.
But I do think building peer-to-peer network instead of proxies is a better idea for circumvetion.