That helps...
This recording is substantially out of phase so where you were hearing the vocals all in the right I was actually hearing everything in the right (this is essentially how one hears a severe phase shift - the leading channel is all you really hear/perceive, the trailing channel is basically dead).
So mixing wouldn't fix your issue and most likely isn't necessary (at least not to my ear).
My quick estimate is the right is ahead about 15 samples, though I didn't play with it much to try to fully verify that. It seems to vary between 11 and 17 samples but 15 was looking like a fairly consistent offset. You can actually try several different offsets on your sample by varying the starting point of the right channel where I note the specific point below and go with the one that lines up best:
So combine the entire set in Audition if it is in more than one part. Convert your scale to samples. Copy the right channel only, then with the right channel only selected go to the point 15 samples or so in and right click on the right channel only > Mix paste > replace. This will move the entire right channel back by the number of samples you pasted it at and get them in phase with each other.
Now you should hear both channels more or less in alignment and that very annoying effect you had will be gone. There is substantially different content between channels but it seems quite a bit better after that. I sort of suspect your left mic wasn't pointed in the same orientation as the right (or you were seated or standing somewhat sideways in orientation to the stage/sound sources).
You also have a substantial DC offset in the sample. Correct that by highlighting the entire thing (both channels) > effects > amplitude and compression > amplify/fade (process) > center wave preset
Your left channel is nominally about 1.5 dB weaker than the right. That will also make the left seem overpowered by the right. I hear no reason not to boost it to even them. Of course when you're done with everything the whole thing needs somewhere over 12 dB to get the levels up near 0 dB, so you can balance them by amplifying them each once separately to par (which may be a better process).
Here's the scratch sample with those quick adjustments so you're hearing apples to apples between channels (not with the final amplification though):
http://we.tl/1KgHOf0D6EHTH.