Unless it had been included in a recent firmware update for the EOS 5D Mark III, the only Canon model (as of June, 2014) capable of applying Exposure Compensation to Auto ISO in M exposure mode is the EOS 1D X. That capability was not included in the original firmware but was added by a relatively recent update.

Since this answer was written, several new Canon models have also included the feature: 7D Mark II, 5Ds, 5Ds R, 1D X Mark II, 5D Mark IV, 80D, etc.

Have you tried using the different metering modes available? If you are using evaluative or center weighted averaging the camera is brightening the exposure because it is trying to expose the entire frame, including the dark areas away from your primary subject, properly. Partial and spot metering will only use the center of the frame to calculate exposure. You may need to frame wide and then crop later to get the composition you desire but this method also has the advantage that focus performance in low light is usually better near the center than at the edges of the frame.

Although it isn't the ideal many Canon shooters (including myself) desire, here's what I do in similar situations.

1) I shoot in Av exposure mode, put the ISO to the highest setting I am comfortable with (based on the intended use of the images) and keep an eye on the Tv in the viewfinder as I shoot. If the Tv gets too slow I use the Quick Control Dial (the large dial on the back of the camera) to adjust Exposure Compensation

2) I shoot in M exposure mode, select my Tv, Av, and ISO and live with the occasional over/underexposed frame. RAW files are very forgiving with regard to exposure: I often increase or decrease the exposure by up to two stops in post production.

Face it, the situation described in the question is one of the most challenging a photographer will deal with. It is a little unrealistic to expect every frame to be perfectly exposed. Even when using a camera with EC applied in M mode with Auto ISO selected there will be times when the lighting on stage changes drastically in the split second between metering and exposure.