Northern Idaho (around Moscow) is some ruff country. In less you lived and hunting there I certainly wouldnt suggest doing it alone.
You have friends that dont hunt. Good that will get you to Moscow. But what from there. How you going to get into the mountains? Horse, 4 Wheeler, truck? I doubt you're going to have much success staying in Moscow at night and getting into the elk area at shooting light. I would think you're going to have to camp.
Shooting an elk isnt a big deal. But then what. They have to be dressed and packed off the mountain. Then the meat has to be frozen for the flight back to Ohio. How long is the flight, how many lay overs.
Guide buddy or what ever, unless you've hunted elk in the past you need to take someone with you.
Ever thought of the Wyoming Big Horns, They are high, but when you get on top they are rolling hills. At Burgess Junction out of Sheridan they have a lodge (Bear Lodge) right in the middle of elk hunting that have reasonable hunters rates. You can fly into Sheridan, rent a truck and hunt from the high way. West a few miles from Bear lodge the Tounge River is on the south side of US14A. find a likely spot in the evening and glass. The critters come down out of the timber to water and feed on the willows. Set there on the rail fense and glass. You'll see critters. May not be the best but its the safest for one who is hunting alone for the first time. If you see and down an elk, it will be in the bottom, but not too bad getting the chunks back to the road.
I dont know since I do my own butchering and live here, but i think you can get the Bear Lodge to freeze the meat for shipping. Dry Ice is best, but you cant fly with dry ice I dont think.