Another option that's a little higher end is to use a dedicated video production rig, and feed that into your computer (or use the rig's direct integrations). Something like a Tricaster (
https://www.newtek.com/tricaster/), which is very popular for live event video production.
The more complex the setup, though, the more likely you'd need additional people working the controls. (But also, the more flexibility and conveniences you get).