Any YouTube videos that you can reference so we have a sense of whether this is a dance routine, a skating routine like you might see from a band on a field, etc.
I'm having a hard time figuring out what you will be shooting.
I'm supposed to get a CD of what was done last year, but from my discussions it sounds like it'll be similarly lit like this: https://www.youtube.com/watch?v=3BpFL1tA6lY
You're screwed. But give it the best you got.
I would spot meter, I would only focus with the center AF point, I would probably also lean toward the 135L f/2... for the extra stop of light, and because it has a really good AF motor. I have an 85L mkii and anything moving can be a challenge, so the extra stop and change wouldn't help me because everyone would be blurry.
For that type of show... you can't use flash... but you can use the spotlight which has to be your best friend. So follow that around. Tripod... monopod... either or... but the 135L, the 85mm f/1.8, or the 100mm f/2 all lack IS. If you have a buddy in the neighborhood with a 200mm f/2 IS, that might be your best bet. Feel free to rent, but this is a challenge and a 1/2 regardless of the body and the lens combo.
The other day in the dark I was using the 5D mkiii and I had to resort to only using the center AF point because it was the most sensitive. So the other 76ish points won't make a huge difference. So I'd probably lean towards the 6D as well.
I'd also suggesting using something with the IR beams for focus. I used the yongnuo 622c transmitter even when I wasn't using off camera flash, because the ir beams really came in handy to lock onto your target... having said that... a red grid on the performers might be distracting to the show...
Also, see if they will agree to wear a white and black checkerboard outfit... because that will also help to lock focus.
I'd shoot in manual, set your shutter speed, open the aperture wide, and then let the camera adjust for iso... For movement, I'd agree that 1/500th is better... but I might try to get away with 1/250 if they are slowing skating... but getting those shutterspeeds... again... good luck.