Many, many, years ago four of us back-packed four miles into the Flat Tops Wilderness Area. (This was before it became infested with the big orange flowers every fall.) Our camp was by Big Fish Lake at about 9,600 feet up. This was our 2nd hunt out West for all of us, and we drove from Michigan to get there.
We ended up shooting three bulls, two were about a mile further into the wilderness and the third was about two miles further in. We skinned, quartered, deboned and packed meet for the better part of five days to get them out. On our first trip out to the road we went into town and bought lots of bread, butter and pepper. We ate fresh elk steaks for breakfast, lunch and dinner for five days...the more you eat the less you had to carry!
And I still lost (8) pounds.
We parked our trucks in the parking lot right on the main road and it was full of trucks, campers and tents. The majority of the hunters in that area prefered to camp on the road, walk into the woods about a half mile after daylight and walk out before dark. As long as I live I will never forget the looks on all those hunters faces when my brother and I came hiking down out of the mountains with two respectable 5x5's on our back-packs. We were so proud...it felt like we were walking on air (even though our packs weighed about 90 pound). I still smile when I think of that hunt.
Would I do it today? Hell no! Getting a little too old for such foolishness. ;-)
To answer your question...I wouldn't recommend going farther than we did. But it all depends where the elk are I guess.
Good luck!
GrizlyHunter