Welcome aboard! I'm kind of hesitant to offer advice, since the habitat of KY and VA are vastly different than my experience (western U.S.). However here are some ideas/thoughts.

Elk tend to be more active around dusk and dawn, especially if the nights are warm and you have good moon coverage. Basically they will just lay up all day since they fill their bellies at night and don't have the cold to fight. I'd hunt the dusk and dawn hours harder.

Elk, like whitetail, do rut and since they are transplants from the west, perhaps they still have a rutting period similar to western states (september). Scouting at this time would be great, since vocalization (bugles, cow calls) go way up and the sound really carries. Given the temperature and elevations differences though, its possible that maybe they rut as late as December in your area, although I really have no idea.

I'd look for fresh elk sign (tracks and scat) in the areas you think they frequent as a first indicator if your getting close. I'd probably just walk the banks of some water ways in the area to see what you turn up. Elk tracks are hard to miss.

Around here where water is less of a commodity hunting water holes in a dry fall can be used to great effect. This might not work for you though, since I'm guessing water is probably easily accessible, in which case there maybe no pattern as to when and where the elk get a drink.

Good luck, sounds like a challenge.