You should have skinned the deer and cut the head off.
Meat will not go bad in a hour or two - so the most important thing is not to get it cooled down, but to get the hide off it as quickly as possible.
Most taxidermists will tell you that if you hang your buck by it's head, it ruins the cape - if you want to get the deer mounted, because it stretches the neck muscle and the cape and it makes the neck smaller in diameter and longer.
It is a pretty awesome buck, how many months were you watching it before you shot it. I think you must have had it all planned out - if you spent all the money for the meat locker up front and all the time to build it before the season started. Good Job.