For what it's worth, I've never been actually penalized for streaming on YouTube. Sometimes songs get muted or it just won't stream in certain countries, but nothing on my account.
That said, Discord is exactly what I've seen people use to get around this issue. They'll stream the chatter parts of the show on YouTube, Twitch, or whatever, and have a private Discord open with an invite in the chat. Once it's time to play music, they swap to hold music in YouTube/Twitch and stream the actual music on a channel in Discord. Voila.