Most of these things are poorly and unevenly lite, or for artistic reasons have sections that are very dim. I keep saying to myself its not my problem because I'm just hired to capture what I see but it always seems to become my problem.

I end up having to spend a lot of time adjusting the brightness in post. I do my best not to wash out the highlights both in shooting and editing but customers often complains its too dark. Forcing me to go back and readjust the brightness again to their liking. If I didn't know any better and saw my own work I'd say its grainy and over exposed even though I have high quality equipment. It also makes it impossible to set the exposure for an unmanned camera if the brightness from scene to scene greatly fluctuates. I've even got into the practice of warning the client before hand but they still seem critical of the results.

My last client complained it was too dark and when I asked what tv she was viewing it on she said a computer and a digital projector. This after spending the time adjusting the brightness on a crt tv monitor. Grrrrr! I wish I could tell the client to look else where if they think someone else can do a better job or pay me more to re-edit, but I need the business and I get the impression they feel they're entitled to get a video that satisfies them after paying me $500+.

even though I have high quality equipment.

What cameras?

Pete, have you tried using the spotlight mode (if you have one) for the unmanned camera?
Ive used it before with the canon xh-a1 and its very good for an unmanned camera.
Ultimately though if the stage is black with just a dancer holding a candle( been there!) best you can hope to do is get a close up with the other camera and just live with the shot from the locked off one.
The problem is that most of these dance shows are lit for the audience as you say and the video is not considered, even filming positions are of lower importance than cramming parents into the halls so perhaps negotiations prior to the event can help to sort out the lighting and filming locations.

What cameras?

Sony Z1u is my main camera, Fx1 my 2nd, and if I need a third I hire someone.

For my last performance, the hired guy was using the Panasonic Hd200x (no sure of the model number) but he was shooting auto exposure and as a result over exposed most of the performance. And a 3rd person shooting the long shot left it at the same manual exposure for the whole performance. Which brings up a separate issue of finding help who know what they're doing who don't cost a fortune.

Welcome to the wonderful world of theatre lighting. In many cases, the real snags are that whatever lighting youe see at rehearsal bear little resemblance to what you'll grt during the show. If you are stuck with an unmanned camera, then with a fiendly lighting man, you might get if you ask, some of the real states that will be used - BUT, you rarely get follow spots until the show, and they kill everything. You need information - so if there is going to be unsoftened followspots added, you'll have to set a maximum manual level, back it off a bit and hope. The spot setting is a help, so is a tweak to the knee circuit if you have one, to lift the blacks a bit. Cameramen with a quick eye and good manual adjustment are the key to success - and double check of the followspots are discharge types, they can be very blue - so white balance adjustment is going to be a compromise. A white tutu in a ballet solo can look very odd.

If you have cameras that are iffy in low light and need extra gain, use them for close ups where the subjects are well lit - they won't do very well with wide dim shots.