If you're going to tan it yourself go to brain tan.com and learn a bit about the "old ways." Brain tanning an elk hide is an excellent experience in patience by the way. Back to your skinning first though, lots of folks make the leg cuts on the inside of the animal but if you cut on the front side of the front legs and down the back side of the back legs you'll get a more uniform sized hide, again that site about brain tanning can prove that to you. Be very careful not to score the hide when you skin, as any scoring will be a weak spot in the leather. Many people like to "punch" off the hide when the animal is still warm, works well on a deer but you better be strong to do it with elk. Which ever way you get the hide off its better to leave extra meat and membrane on it than to score it. You'll be spending a few hours with a drawknife removing flesh and membrane anyway so skinning really clean isn't the way to go.
Now about hair slippage, if you want to tan the hide hair off slippage doesn't matter so fold it skin to skin and you can leave it like that for a day or two in warmish weather. The longer you leave it the more it will begin to stink but also the easier it is to remove the hair.
If you can't get to the hide right away toss it in the freezer, don't salt it ever if you want to brain tan. If you can't freeze it then remove the big pieces of flesh and ideally the membrane but this can come later, lace it to a frame and let it dry, it'll keep that way for a long time indeed! In fact if its nicely scraped and dried keeping it for a couple of years will make for a much softer brain tan in the end.
Another thing you can do is simply make hair off rawhide and that stuff has a lot of uses too, its easier to make and if you ever want to brain tan the rawhide you do have that option.
I could go into the whole process but it would take too long, it's a very rewarding experience though making your own leather from an animal that you killed yourself.