Look at the open end of the socket (the end that fits over the bolt head) and you will see the first 1/16" or so is a chamfered lead-in section that does not fully engage the bolt head. You can grind the end of the socket down until that lead it is gone, and the flats that engage the bolt head are right out to the end of the socket.
If this does not address your issue I may not understand the problem. Take a couple of pictures and post them so we can see what you are encountering.
2001 Bonneville SSEi (retired at 365,000 Kms.)
2014 Jeep Grand Cherokee Overland (yes, I know its not a GM)