As I see it, you didn't put in for the drawing, so you are looking at going the second rifle season or later with a gun. At that point, unless the weather/snow forces the elk to come out and play, it can be very hard to locate them, especially on your first time in the area. If you get some decent snow, then you may do well. However, you have to remember that at least 3 elk seasons have taken place before then (archery, muzzleloading, and 1st rifle elk). If you get warm, dry weather, you may be for a lot of elkless days.

I know the odds would be long on a bowhunt, but you can buy the tag OTC in MOST areas (not all) and you will be in the mountains when the aspen trees are golden and the elk are singing. Can't beat it. I guarantee you that if you see/hear some bugling bulls, even if you don't get a shot, the trip will be worth it. Might give it some consideration.

What unit did you go mule deer hunting in? Since you already know that area, maybe someone with knowledge of that area can tell you if it is worth your while to hunt elk there.