Not sure how much work this would be but feel the interest in an extension like this would be fairly large. Anyone working on something like this or willing to?
I will do the same.
The Problem is we need to know what kind of equipment you have.
The easiest way is you use Twitch or something similar.
There are some Provider who could make everything for you.
You add some HTML5 Webplayer to your Page and the Company do the rebroadcast thing 99% hidden.
For example that Company do the Streaming Service for the Austrian Television (ORF).
Maybe its cheaper when you talk to an ISP and host your own Server.