The one issue I’ve found is that most services seem to retain _much_ less precision for participant video versus screen sharing. Text can often become really blocky and blurry.

I did something similar, but used OBS. There are a few ways to feed video from a cell phone into it. Gives you the chance to do any zooming/cropping/etc to account for limitations in where you can place the phone. As well as adjust brightness/contrast/white balance if you’re really anal about that kind of stuff.

From there I open the feed in a “projector” window and screen share that.