Parking should be based on where your seats are, generally, If you are in in 101-120 park on the east side (Route 20) , 121 to 143 west side ( Route 20A). You can use the same logic with the upper deck.
I have been doing to Bills games for 40+ yrs and figured its better to walk an extra 5-10 minutes than spend 45+ minutes in the lot. i would go to a private lot and tell the attendant that you have a long drive after the game and need to leave quickly, I will often slip them $10+. This has never failed me.
I also live in NJ and have the same Giants issue (lol) and know your pain.
PS-take them to the Hammer Lot. He will be a Bills fan for life!