We have used a non-PC variation on the theme of dragging the animal or large quarters out that a buddy of mine had heard about. It's sort of like a roll-up toboggan, and has worked in moderate hills the few times I've used it. Take one of those 6' "magic carpet" sleds, then punch holes and set tarp grommets across the front and down the sides. Use something like shot-line or parachute cord to lash the deer on. I lashed the head and forelegs together, secured to the front of the sled and to the drag line(s), and it worked just like you described, with the bonuses that the poly-????-ene gave very low friction with the ground and protected the hide.
I wonder if a PC version could be made with waxed canvass or leather?
If I got something BIG and/or farther back, I'd favor boning it out as much as we can with our evidence-of-species-and-sex-attached regulations, and drag if I could, pack if I had to. I haven't had the occasion to do this since I read about the field-boning and/or "gutless" techniques.
Regards,
Joel