Because Hornady will only make ammo - no brass for reloading - you will have to find someone willing to part with cases - tough to do - or pay $65 and up for 20 rounds via AmmoSeek.com.
This is the shortcoming on "better, new cartridges". Hornady is too busy bringing out the latest one (1, 2, 3, 4, 5, 6, 7, 99 PRC) to be bothered with properly supporting all the people that fell for their marketing a decade ago when the "better, new cartridge" was the .375 Ruger.
I can get 2700 FPS/56,000 PSI from my Ruger Alaskan's 20" barrel with W760. That puts me at 10% under max pressure in a nice harmonic node with the 270gr SP-RP or Barnes TSX. A 20" barrel was ALOT easier to still hunt with, and handle in general, than the typical 24"-26" H&H barrel. The .375 Ruger is significantly better than the H&H IF ONE IS STARTING OVER OR FROM SCRATCH. I wouldn't sell an H&H to switch horses here. I didn't have an H&H when I bought the .375 Ruger. I will eventually buy a .375H&H just to have the classic.
Either you have to be shit hot rich to buy boatloads of 300gr factory ammo, or you have to be willing to handload/reload factory ammo as you can scrape it out of your budget. (My case, for sure!)
If you tell your PH you are bringing in a .375 Ruger when you reserve your hunt and ask them to insure they have 40 rounds for you in the camp, I bet they will back you up.
Go with a buddy who is also taking .375 Ruger, and then the airline has to lose two guy's baggage.
Also, book your connections 3-4 hours apart so the people in baggage handling can get your bags onto your connecting flight. Our ticket agent tried the 30 minute connection flight crap and we had to start all over on booking flights. Good thing we did - we would have missed the international flight out of Newark, as we were 30 minutes late getting in.
The .375 Ruger is a better cartridge, but the games in the industry - Winchester and Federal not making any of the ammo, Hornday not making components - are hurting it. It will still be a while before the ubiquity/availability of ammo is adequate. However, if you want to use the Ruger, you can make it happen. The .375 H&H will get the job done too. You pick and TRAIN with the rifle before you go!!!!