In both my of my 375's (a CZ550 and a Winchester Highwall), there is what seems to me to be quite a bit of freebore. There's roughly a quarter inch (yes, .250) between seating at the cannelure vs. seating to the lands.

When I seat at the cannelure, accuracy stinks.. when I seat ~.050 off the lands, things tighten up nicely. I know the obvious answer is to seat .050 off the lands, but in most cases, this means less than .375 seated in the neck and I'm pushing the limits on magazine length in the CZ.

Is this much freebore normal in a 375?

They have about that freebore as standard.

Try full sizing the brass so you have a few thou headspace. Very often neck sized shoots best with bullet near the rifling and sized brass with headspace will shoot best off the rifling. Quite often using a faster powder like 4064, Varget or Reloader 15 will get you the results you want.

Different bullets might help. For example, 270 grain Hornady spire points drop below bore diamter in front of the cannelure and so you get the full freebore.

But I have had loads in 375 like you that would not shoot at the 3.6" OAL. Last one was with 270 Speer spitzer but that was a Wby Mark V and have a long magazine. You should be able to seat out a little further than a Wby, they are about 3.8" magazine and I think CZ is 3.85"

Just in case someone chimes in about how well their 300 Wby or other Wby calibre shoots, Weatherby freebore is different. It is a parallel section that when done right is only about half a thou over bullet diameter.