One of the cartridges on your list that is a great cartridge, although some folks have written off is the 7mm WSM. It really doesn't do anything the standard 7 mag does do, but it is a very accurate cartridge. I will generally slightly outperform the standard 7 in velocity with bullets up to 160 of so grains, and does it with a short action and shorter barrel.
I don't have any problem finding ammo for it, when its available I buy it, and I save the brass for later. I also have a 257 Wby, its a fun cartridge, but for some reason the 7mmWSM is really just more interesting to me. Since the first time I zeroed the rifle, I have been amazed at the tiny little groups that it shoots. It is loud though, and the recoil is noticeable.