The job of the overheads is to pick up the bulk aggregate sound of the entire kit. What I usually like to do is not put those mics over the drum kit. You can play around with putting a couple of mics in front, or maybe one mic a few feet in front of the rack tom and another off the side of the floor tom. For one thing it will pick up less attack from the drum heads but a lot more of the shell tones. Cymbals radiate sound up and down so it should do a lot to tame that as well. Doesn't seem to have much effect on the hihat. The best way to turn that one down in the mix is get the drummer to not hit it so hard.
Might be worth a try. In any case moving the mics around is going to have a big effect on what gets recorded.
