I learned the hard way that multiple cameras can make things interesting. More in that in a moment.

"Faces are washed out" tells me there may be too much light - though I guess it is possible there is not enough.
Noisy video tells me there's not enough light... I guess I need clarification on what the lighting is.
What do you mean by the camcorder being "faster"?

If you are happy with a single, static, wide shot, then either of the camcorders on your short list meet your requirements and may work just fine. The HDR CX900 is 1080p; the FDR AX100 is 4k.

About multiple cameras...

If you do a single camcorder, then you end up zooming and panning. I don't know how much room you have or what you want in the way of captured video or how active you want to be during the capture... but after a few years of a single camera, I got a second one... camera1 has the wide shot - basically what you are getting today. Camera2 gets close ups. You can add a third camera, too. You merely need a different camera angle... so, in a 2-camera shoot, Cam1 is in the middle, wide shot. Cam2 can be right next to it, but it gets closeups during solos (or whatever or even crowd shots). If you do a 3-cam shoot, then Cam2 goes to one side of the stage.

The fun comes with editing. Use a video editor that can deal with multiple simultaneous video (and audio) tracks. Sony Vegas and Adobe Premiere for Windows; Apple Final Cut and Adobe Premier for Macintosh. Synch the audio... when the echo is gone, you are in synch. Use the wide shot cam1 as the "main" view. The other camera views get cut where you want. It is actually pretty easy once you've done it. You can get fancy and cut in rehearsal or any other video you want.

An investment in some lighting and light trees and using same would make any video capture device (even the CX220) perform better. This could be as simple as a couple of light trees and 4-6 par cans or something really sophisticated. Maybe that is something the band would look into?

The Sony HDR-CX220 is an entry level consumer camcorder. The lens diameter is small and can't allow lots of light into the camcorder's imaging chip... then, the imaging chip is small so it can't deal well with what little light does come in through the lens. If lighting is poor, then the camcorder will try to compensate by opening the aperture, slowing the shutter speed and increasing the video gain (basically, "light amplifiers" associated with the imaging chip). Mash this together and the low light environment causes "video noise" (what you call "grainy"). The CX220 has no specification for lens diameter because it does not have threads to add a filter. It is probably in the 30mm area. The single imaging chip is 1/5.8 inch. Compare this to the 62mm lens diameter and 1 inch single imaging chip of the CX900 and it's 4k cousin, the AX100.

Camcorders with large diameter lens systems and large imaging chip arrays get expensive (good glass and big chips cost). Note that as the camcorder increases in price, the lens diameter and imaging chip size increases. Manual controls start moving to the outside of the camcorder rather than buried in a menu. (I was in the same space you were a few years ago and went from a Canon Elura 65 (30mm lens diameter, 1/4.5 inch sensor) to a Sony HDR-HC1 (37mm lens diameter; 1/3 inch sensor)... then to a HDR-FX1 (72mm diameter lens; 3CCD 1/3 inch imaging sensor array)... and now use a NEX-EA50UH (67mm lens diameter; 1 APS-C imaging chip), HDR-AX2000 (72mm diameter lens; 3CMOS 1/3 inch imaging sensor array) and HDR-AS30v action cam... hence the "slippery slope".)

Audio is another item and you did not indicate you're having issues with that. This is good, but I would expect the loud audio to overwhelm the automatic audio gain control in the CX220. This would cause muddy audio, potentially with static (when peaking) to be recorded. The new camcorder should have some sort of manual audio gain control - or use an external audio recorder (i.e., Zoom H1 or H5).

Anyway, before I suggest a single up-to-$2,000 camcorder, I want to explore your thoughts on possibly a couple of $800 camcorders... + multiple tripods, cases and maybe lighting... and perhaps a video editor upgrade...