Gutless...
Split the hide up the middle of the back, skin one side, spread the out hide fur side down. Remove and bag the backstraps first, then move on to the hind quarter. I de-bone and lay the meat on the hide. I bag the meat as I finish each quarter, hang if there are trees nearby and work the next quarter. Roll the elk over and repeat. After that meat is all bagged and hanging, make a small slit and carve out the loins.
If you're planning to use the hide for a mount, there is still plenty of hide to use to lay a boned out quarter on. Or as mentioned, carry Tyvek or a space blanket to lay the meat on.