IMO, its just as easy,to get the skin off going up the inside as opposed to up the back. Just a bit more skinning on the belly. It also makes for cleaner working and less hair on the meat.
Get it on its back, make a cut from under the chin to the butthole, Ring the legs at the knee, but don't cut the legs off yet (use them for a handle/leverage), skin up the inside of the leg to the crotch/armpit to the initial cut. Peal it all off. With the hide off like this, you have a large clean area to work on. Try to keep it clean, and don't step on it. Roll it up as needed. The only downside is the blood can pool on the hide depending on the shot and how its laying. Not a big deal on elk/deer/bears, but on animals like antelope and sheep, the hair is hollow and will soak in and stain it, so wash it out and hang to dry ASAP.
I had a flat skin tanned off a winter caribou bull I shot a couple years ago. It turned out great, and was super easy to get off.
I've always wanted a nice elk flat skin as well. Those early winter coats are super soft.