Well, in MT, we used to do this thing called dragging them. I drug a deer like 3 miles once so we wouldn't mess up the farmer's road! Fortunately it was downhill and I was in peak condition. I drug it about a mile to the road and the the farmer is like, well, we are so close to the house, you might as well drag it the whole way!
If desperate, one might cut it in half before dragging it out. Elk are BIG!
If you see a REAL hunter carrying only the head out first, it is simply a choice. In wilderness, there are lots of hunters. Most non-human. You have to make a call. FR quarters, RR quarters or cape and head. Most carry the head out as a big one is not replaceable and is a lifetime achievement. You don't want to lose that to a wolf. In some areas, you might be able to get a replacement tag if they eat your meat. . .not sure. You are still going back for 2 more trips. . .or paying a guy with a horse for some help.
Also, here was the deal with meat for me. With Elk coming last, I usually had 2 antelope and 2 deer in the fridge, so I had some meat. . . .actually enough for the whole year. I think when we got too much meat, we donated the cut Antelope to the local mission.
Last, on TV, they have people call bearer's. Look up bear and you will know who was carrying the Elk!