Hey Bear,
My friends and I have been shooting Remington Rifles in 22-250 for many years with great success, and performance. We have worked a load that will shoot in the dime size for 5 rounds, if you can do your part.
I also have some friends that use the Win. 243 and one guy that is really serious about yote hunting, He uses a custom built 6mm Rem. but he has to sew alot of hides, but it carries better in the wind, he hunts in the Owyhees on the Oregon side, south of Jordon Valley.
I saw one my friends shoot yotes out to 500 to 550 yards, one shot, bang flop with my 22-250. I have also taken rockchucks out to 400 yards, (but that is a story for another time) If you are going to hunt the Idaho desert, and make long shots, and you want to keep the pelts, I would consider nothing smaller than the 223, but would lean toward 22-250, 243 Win, or 6mm Rem, right out of the factory box.
I don't see that a custom rifle is going to make a difference, when the bullet hits the boiler room, they won't know the difference.
I don't know if you are a reloader, but you can load the 243 & 6mm with light bullets (60 & 65 grains)that will not leave an exit hole. We have loaded the 22-250 with a speer 52 gr. hollowpoint, most of the time it will not exit, only when they are within 100 yards.
But on the other hand if you can get the yotes to commit to 200 yards or less, the 223 is an excellent round, and now I am reading alot of good reports about the 204 Ruger, but have no expereince as of yet, I will see about buying one this next year. My 2 cents, I hope it will help you out.
Good Luck and God Bless You,
IDB