Don't give them a chance to move, just call. I had this problem at my old house, and it gets really old trying to guess where the person who is blocking you in is located. And I am calling even faster if it's a neighbor who obviously knows they parking in front of their neighbor's driveway. There is simply no excuse for blocking, or parking in (yup, this happened) someone's driveway without permission. After a while, you just call if the driveways blocked. I relish in costing these assholes money.
Driving home a few years ago, I had a ~19yo lady parked IN my driveway. After a long search, I found her visiting a neighbor across the street. When I said, "Hey, what the hell do you think you're doing?!", she looked at me like I was crazy and actually said, "Well, what do you want me to do? There was nowhere else to park!"
We are doomed.
The post would have been better if you told us the vanity plate, and had it be something ironic or especially fitting - even if you had to make it up. Maybe COKBLOC or something.
We are doomed.