Hmmm you would need a way to communicate which notes are from the private relay and shouldn’t be reposted. Then have to trust those you invite not to re-note. Communicating privately might just continue to be the easier way. 

 Private chat groups definitely a better solution 

 I was going to say..wouldnt this just be a group chat on Nostr? 

There's chat features around topics, couldn't a private relay host one of these chats with a given hashtag or identifier? 

#asknostr