jrodgs I'm actually working on an article right now about this very issue, called Manual > Auto. 😎
I don't recommend using auto exposure in a live environment with stage/theatrical lighting. There are too many moving parts and cues that can cause these types of issues.
I would recommend you start working on a way to stop using auto exposure and work on lighting adjustments and ways you can adjust exposure manually.
I know that lighting for the room is different than lighting for video, but sometimes it takes a bit of compromise on both sides to get something that works well. It's really hard to go through an entire service without having to adjust exposure, but you can at least make the jumps less harsh in a few different ways.
You may want to start teaching your camera ops how to adjust iris smoothly while running camera - either on the lens ring itself or with a LANC remote that has iris adjustment. Or you can use the Canon RC-V100 remotes to give you remote control of those adjustments from a control room or booth.