I'm a choir director by profession (photography's my passion!), and I frequently record concerts both for myself and for other directors in the district. Since I do it for free (part of my "job"), I try to make it as painless as possible. I shoot with a Tascam DR-60D, 2-3 external mics, and either my 6D or 70D. I shoot only the songs themselves, and feed the mixed audio into my camera so the sound on the video file is pretty good (most times I can simply use that audio for the final mix), and that makes my job much faster in post.
If I were in your shoes to make it easy, I'd certainly use your external mic for the audio, and while I'm not very familiar with the EOS-M, you should be ok with it for video, especially if you stick to shooting only the songs (breaking in between individual songs or groups of songs). Keeping the individual record time down will help ensure your file size never gets too large (or too long), and can also help with your camera heating up. Also, make sure you're using a fast enough card to record at the rate you want. I would be far easier on you if you could feed your decent audio straight to the camera, as this would (or might) eliminate a more complicated step in post, but you'd most likely have to give up monitoring audio, which is a tough trade-off...
Anyway, the way I see it you're already doing much more for her choir than they currently get, so that's something to keep in mind.