2000 ISO will be achieved within the camera by shooting at 1600 ISO and then digitally pushing the file by 1/3 stop to make it appear as though you were at 2000 ISO. Not only does the digital push increase noise, but it throws away 1/3 stop of highlight headroom. You would be better off shooting at 1600 ISO, underexposing by 1/3 stop if need be, and then doing your own push of the raw file later. However, if even 2000 ISO is leaving the shot underexposed then that's also bad. Consider increasing the ISO to 3200 and making sure you Expose To The Right.
Again, I've no idea what the scene you are shooting looks like, but you may find you can shoot the 10-22 wide open and still have ample DOF. It is, after all, an ultra-wide lens.
Going back to the noise side of things, make sure you disable HTP. It should be off by default, but worth double checking. Also, while the file may well look noisy if you pixel peep, how does it look when viewed as a whole image at once? What raw software are you using - DPP? Lightroom? Other?
I've shot the 7D at 6400 ISO (indoor basketball) and got IMAGES that are very usable without hitting them hard with NR. However, blown up to 100% the noise does look pretty dreadful. Be sure you aren't disappointed for the wrong reasons.
Here's a 6400 ISO example, with no edits except white balance....
and here's how it looks at the pixel level....
The pixels look crap. The picture looks fine, to me. Last time I looked photography was about making pictures.