The 3-9x won't be ideal on a .22 for the reason already cited.
Otherwise, I don't think you're plan is unreasonable. One of my coyote rifles wears a 2-7x and is just fine, the others are 4.5-14x FFIIs but most of the time I leave them set on 6x. I get some long shots in now and then, but most tend to be between 75 and 150 yards.