The cheap and easy solution would be to just use a personal CCS7 ID as a group call for all participants (not exactly private), or just anything that isn't being used and won't make people mad, on a public network. Not sure how private calls work with DVSwitch, not something I've ever cared to try.

That, or set up an HBlink or some other DMR master server somewhere and directly connect to that.

It's very common, especially on Brandmeister, for people to make group calls on personal ID's to connect, I've noticed.