CZs typically are pretty accurate rifles, certainly better than 3 MOA.
Generally speaking, the primary causes of inaccuracy are (mostly in order):
1. Poor shooter
2. Loose screws (action, scope, etc.)
3. Poor ammo
4. Other, minor things
A box on a picnic table is certainly not an ideal rest for accuracy testing, especially at 175 yd, so you're not really getting a true picture of what the rifle can do off the bench. Apart from that, and assuming you have the fundamentals of position, sight picture, breathing and trigger control well in hand, as well as good optics on the rifle, I would go over the rifle and scope rings carefully and ensure that all the screws are snug.
Then I would try a few different ammo brands and bullet weights. Stick with known good performers, whether in factory ammo or handloads. You can't expect 1 MOA out of surplus ammo (2-4 MOA is more the rule), nor will you get top accuracy out of surplus bullets.
Only then would I worry about cleaning regimen.