How do I replace ceiling drywall over cabinets?
Personally I would pull them down and drywall the entire thing. The edge of cabinets is going to not look very well when your done if you don't and will stick out like a sore thumb. It's easy enough to pull down the cabinets too. 

Also I would remove the drywall from the edge by the wall too and mud the corner. It's going to make it cleaner looking in the end.