Well, I finally got around to sighting in my .375 today. I must say I was kinda dreading it as my factory target wasn't encouraging (@1.5" at 50 meters). First couple of shots were holding that average at 100 yds, but as my powder charges went up, my groups shrank considerably. Best was 5/8", 3 shot group, using 69.0 grains of H4895 and cheap 300 gr. Hornady BTSP's.

I have not touched any of the wood yet, and didn't break in the barrel. So this represents the rifle AS IS, with absolutely no tweaking.
Something to consider with CZ's is that their throats are cut exceptionally long. If you have the option of handloading, the bullet can be seated further out to accommodate this. In addition, all my CZ's tend to like heavy for caliber bullets that can still handle the ROT.
So, even if you don't get a stellar factory target, all is not lost.