Ok great. It is very doable. The thing that is missing is simply publishing a Nostr event of kind 30311 which includes the details of the stream, especially the HLS URL (ends in m3u8). With that, any Nostr streaming website or app including Shosho will pick up and show the stream.
This is already how the Shosho app works - you can add your own server and then when you stream to it the app will publish the 30311 for your stream.
When you stream to your owncast, what do you stream from? Are you using OBS or something else?