I have noticed a few "tactical" 22 bullets coming out:
notice that these are 40gr round nose, I would give these a try. They are pushing at 1200 fps. I would not buy the large package I have above, it was just the easiest to find. I was trying to find what I saw at dunham's but cannot. They were expensive though, and in a large package qty, so if it did not work you were out 54 bucks.