Why not turn the screen freeze into a feature? The kind of thing you have on projectors where you can pause the video in order to show something or leave questions on the board whilst you prepare something in the background. This could be a tool only for the person who is presenting.
To extend on this, we already have a moderator, what if we had a presenter mode. This could either be rights that are given when anyone shares their screen, or the moderator allows users to share their screen and temporarily gain rights.
We also thought about Live notes or sketches on a screen share. This could maybe be abused by students drawing fruit-shaped objects but again this could be a right given by the moderator. The idea is if I’m trying to go through a process on my screen and a colleague is watching, they can “draw” where I need to click or show what they mean without having to awkwardly explain.