If I may suggest 'SchoolMaster: Install all necessary software onto a Windows 10 Pro 'PC' that can be configured to, and left at the chosen EAA instrument setup. A dedicated computer for astronomy use (only) would be ideal.
Then inside using a second 'PC' run Windows Remote Desktop, preferably on a local only wireless network meaning no internet connection. This will connect to, command, and receive camera images for "share screen" Zoom broadcasting. If distance and signal strength is a problem you may need to configure a mount wireless router that can receive and transmit a better signal.
With this arrangement the mount PC will do it's astro things independently from your Zoom/control/internet computer. For my use the desktop wireless connects to the mount PC (running a USB powered wireless router), and the internet link via ethernet to the www router.
Your telescope "window" becomes one of many you would want to refer to during zoom. It's camera view among others like one of the instrument outside or of an assistant helping inside. These all can be an arranged mosaic on Zoom share screen, highlighted as needed, minimized when not. Production complexity to your skill level although simple is a good thing. Scripting and pre-recorded features can help content flow or "on-air" glitches.
Good luck and clear skies.