Buy a quality internal frame pack and debone it where it lays. I hunt several places like you described and I will tell you that from many many times of dragging deer back up the mountain, this is the easiest way.
If you decide to drag it, cut or get a stout stick about three feet long, tie the front legs up around the head and leave about 14-15 inches between the stick and the deer. Turn downhill towards the deer, bend over and backup, dig you fee in and pull it to your feet. Like a rowing machine. Work but not to bad versus the standard dragging method.
Like I said, done both quite a bit and dragged a lot more than the backpack because that didn't used to be legal here, but I never intend to "row" one back up the side of a mountain again. God Bless