From your pic's it doesn't look like the crown goes all the way to the ceiling, although that might be an optical illusion. If yours do go all to the ceiling or to a soffit then the following probably won't be much help to you.

I put crown on our cabinets which are in a kitchen with a cathedral ceiling (kitchen remodel was last winters project). I was playing around with the homepage features a couple weeks ago and there are pics in an album if you click on my user id.

I had the same situation you did with the reveal and I notched the cabinet itself with a japanese flush cut saw so the crown would lay flat to the cabinet around the corners. It only took about 2 or 3 very careful strokes to make about a 1/8" deep cut, and then a couple more strokes to come down from the top of the cabinet to meet the kerf. It turned out fine, I would recommend a few practice cuts on some scrap to hone your technique. Since I had easy access to the top of the cab's, I nailed the crown to a 1x4 frame I installed on the top of the cabinets. I beveled the front edge of the 1x4 to match the angle of the crown.