personally, i wouldnt dig out the grass, just whack off the top that has seeds (or not, if it doesnt) and turn it over with the cultivator. if you've got a machine to do the heavy work then just turn it over, any grass that is left on top pull off, and there you are!!! having a cultivator makes the difference.
cool, I didn't know you could do that! I've never used one, but I'll guess I'll have one of the old ladies there show me how :)