So I would like to add two new divisions of the website.

Adding past broadcasts into a separate archive and revamping the video uploads functions into a third archive (clips, highlights and uploads). All now placed into separate discoverablity sections of the website.

So at the moment everything is jumbled on the platform and user channels.

From a channel perspective it would be as simple as adding these into separate tabs, eg the about and schedule tabs.
That way you can drive more static video content creators to the platform. A rejig and rebranding of the highlights and clips features could also do that trick.
I would imagine this would start as a second place to post YouTube gaming content like achievement guides, walk-through and game reviews.

The way this would impact the main search bar is that you can categorise what content they are looking for by the meta tags on the tabs and content types. Using a red dot for live streams, a clip board for past streams and a popcorn for videos.

I think that this would be very intuitive to most users.