I was also going to suggest the issue might reside with the drummer and how he/she plays in the studio. I also agree with Jeff...processing won't help you fix a track. Record again after having a talk with the drummer and possibly rearranging the mics.
Unless you mic every part of the kit individually into unique tracks, you will have to rely on the drummer to assist in getting the sound needed. Most other players can let it rip and simply turn the volume knob down... drums are a bit different.
With overhead mics... they are closest to the cymbals. If the drummer rides those cymbals hard, that's what you will hear. I played in a band with a drummer like that. He actually broke and cracked his cymbals on a regular basis he hit them so hard. Also shredded lots of sticks on the cymbal edges. Cymbals started and ended every song and if he didn't have cymbals, I don't think he would have been able to play. When our band could afford it, we ended up miking the entire kit so we could hear the rest of the drums. No cymbal mics were needed.
Trying to talk to him about dynamic playing was futile. The cat was good and could keep the groove and backbeat going..... but cymbals..... oh those cymbals.... they were one of the contributing factors to my high frequency hearing loss today.