Yep, nearly impossible on the open market. Occasionally you'll find some brass and ammo listed on the various Classified Ads forums but you have to keep looking as it goes quickly.
I built a few .375-300 WSM rifles a while back but in short actions. I wasn't impressed.
A .375 SAUM will be a little worse than the WSM due to case volume even in a long action.
Now, with a little reloading room magic, You can create the .375 RCM (Ruger Compact Magnum). The .338 RCM brass can be a little hard to find sometimes but it is available.
My favorite though is the .375 Ruger, if Ruger ever gets off their lazy behinds and actually makes a run of brass again. They are way too busy skinning us alive with their ammunition prices to make the brass. Buy ammo to get the brass though really works also.
As long as you're opting for a long action, I've gone to the .375 Norma Mag. This works great and stays within the parameters of the standard long action. You want a long action, use it for a worthwhile endeavor.
Enjoy the process!