I wish you well with that Ruger Alaskan. I certainly hope you don't need to find ammo for it anyplace.
The 375HH has been used in Africa for 100 years, and it's been the staple of big bear hunters in Alaska since before it was a state. I've seen shells for it in Turkey, England, Germany, Mongolia and throughout Africa.
If you want to stay away from a "gimmick" stay with the foundation of all the wolds big game hunting rifles and be done with it. The use of that Ruger design in Africa will take a very long time to catch on if it ever does. It will not be an easy task to push the already well established king of the bush in that caliber out of the way.
I can say with strong confidence that there will not be many places in Alaska that will stock that ammo, and the odds in Afrcia are about zero. You can venture into an ACE hardware in any of the port island cities in SE Alaska and find all the common ammo. You won't likely be seeing any short mags, Ultra mags, Ruger 375's, or any of the specialty magnum handgun ammo.
You will see 223,243, 270, 7mm mag, 308, 30/06, 338, 375HH, ( very limited) 416-458, and a selection of 12-20 gage shells along with .22, 9mm, 357mag and .44mag shells. from there the selection gets thin to non exsistant in a hurry.