As a guy who has loaded for the 7.62x39mm CZ 527M for some time now...might be able to help a little bit. First, bullet fit - .308 bullets will WORK, but they generally won't work WELL. I find bullets that are .310 or .311 work well. Hornaday makes some excellent bullets just for 7.62x39mm, ball, soft point and SST among others. I also use cast bullets sized to .311 with good results. I've used H-4198 with good results, but my favorite is Accurate Arms #1680, which is almost tailor made for 7.62x39mm. The CZ does have a 311 bore.
If you shot corrosive primer ammunition, have you inspected the bore? If you clean normally you should be OK.
Ditch the scope and go irons to reduce variables until you can get the rifle to shoot right, keep it close for starters, I'd say - but, I only use irons with mine anyway, so I'm biased.
Hopefully that will get you down the right path.