Belted cases always head space on the belt.
Generally speaking, this isn't the case for reloaded ammo. If you have a belted case with enough shoulder, better to adjust your dies so you do not set the shoulder back. Now your reloaded case will headspace on the shoulder, which ought to improve accuracy and reduce case stretching.
Specifically on the .375, I full length size my hunting ammo, as I want to be certain it will chamber easily. Also, the .375 is in the minority among belted cartridges in that the long, tapered case has little shoulder, so there's probably not a heck of a lot to be gained by trying to headspace off that. But as far as I can tell, the shoulder doesn't get set back more than a mil or so, making the issue moot.
For reloading, I normally don't use anything less than 270 or 300 grain bullets. The Hornady 270 is accurate, and I can reach 2800 ft/sec without exceeding published data. Cut back to a "mere" 2700 ft/sec and the load is almost mild. For 300 grain bullets, I like the Swift A-Frame (soft) and Speer AGS (solid - costs $$$) for hunting.
For both bullet weights, I've had very good results with Winchester 760 powder.
I recently took a look at a new CZ550 in .458 LOTT and noticed that there were no reinforcing crossbolts in front of and behind the magazine. This is not good. The last time I hunted in Africa, the PH had BRNO rifles (the CZ550B's ancestors) in .375 and .458. Despite the presence of an extra recoil lug on the barrel, I spotted that both of his rifles were beginning to split the wood around the magazine well. You might consider having a good gunsmith install some recoil crossbolts in your rifle before you have too many rounds through it. (If you're handy, you can do it yourself. Check the Brownell's catalog for parts.)
