I have no experience of

I have no experience of filming theatre but I have been comparing you requests for a Canon camcorder. I have had a Canon Legria HF G30 for videoing wildlife and would think that it may well suite your needs. It takes stills as requested during the video process and I have just tested it and it will work without a battery with its in the box battery charger used as a power supply. I have run it for more than an hour so that doesn’t appear to be a problem.