If you get the opportunity, try some Varget with 168g. Sierra HPBTs. 308s seem to love it.
I use Lapua brass, CCI Large Rifle Primers, 44g Varget, and the 168g. Sierra HPBTs mentioned above. I seat the bullets about .007 - .010 off the lands and the results are fantastic (at least for me anyway). My best 5 shot group at 100 yards so far has been .233, and I'm certainly not the best shooter out there. Note: this combination is for my Savage 10FCP, but I'd bet it would work in a CZ just as well, except I'd start at 41g (see the Lyman 48th edition) and work your way up. Best of luck finding that perfect load for your CZ. I have the CZ 550 American in 6.5 X 55 and it shoots great. Love those CZs.