My wife's in a remote master's program. What they did is chop up the lecture. When students asked a question, that was omitted from the online presentation. The result is that an hour of class winds up being, say, four 12-minute videos.

That sounds weird, and it can be a bit choppy, but it has advantages. You get to stop and think at the points where others needed to ask questions. You have natural breaking points if you prefer smaller-sized bites.

So, I don't know if the students are in all of your video, or just when they ask questions. But if it's only when they ask questions, you might consider this approach.

Aww, sad :(. The faces are likely problematic, but the voices themselves shouldn't be (not identifiable to a person)