A gambrel would hang the deer head-down. The heart and lungs would be trapped in the rib cage and would need to be lifted out. If you hung the deer from the head and front legs, everything would fall out. I've done this once. I just gut my deer on the ground. If there is a slight hill/mound close by, I will drag it there so the back of the deer is lower than the front.

I was literally taught how to gut a deer by a surgeon. He did a very precise job.