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.
Quick question for a newbie. I'm just figuring out the field care as I'm new to hunting. Although, I've spent a lot of time in the backcountry. If the temp. is up. Say in the 60-70 deg range. Would using the gutless method be a bad idea? The other articles I've read says to gut and open the cavity to cool it off. I'm just wondering if using the gutless method would cause to much heat retention while I'm getting the meat off the bone and ready to dump in a creek.