H2H7 / i found a way for players to organize streams for their team.

my idea is to host streams through Cyutube. Cyutube is basicly a thing like twitch only with the exception that it allows you to take other media such as youtube and put it on your own cyutube server for you and a select group of people to watch. here is the list of media providers allowed on cyutube, as you may be able to see you need to simultaneously stream it to another media provider such as twitch. however if everybody were to create an account on a website such as U-stream which doesn't give away who they are and people do not specify which game they're playing it is possible to hold private streams for your h2h team members 

That doesn't sound like it makes anything any more private than U-stream would be on it's own. So I don't think that'll be allowed.

Doesn't Skype have an option where you can let the other caller view what's on your screen?

A real option for privacy is using the steam version and steam's broadcasting features to filter out anyone but those on your team from viewing.

The Skype option sucks hard. At least that´s what I experienced in the past

All I know is that I hope people still find ways to stream other projects during H2H. Streams really do bring the community together and it would shame to go without them for a long period of time.