I've raced mine for several seasons on Michelin S12 130/80 rear, cant remember front size but an S12 it is. I changed to a Mitas 130/80 at the end of last season, think I like it better than the Michelin. CZ's run the chain quite close to the edge of tyre so you gotta keep an eye on that, I've got about 3-4mm clearance & not much more on the other swingarm side. I've been known to take to the edge knobs with the grinder if it looks too close. You don't want any sideways wobble/warp on the rim either so it pays to roll the wheel thru one full rotation & check chain to tyre clearance.
Kiwi conditions may vary from Oz, but generally soft terrain tyre is best, if the conditions were hard to start with you can gaurantee it'll be getting real soft as the day progresses. Only time I've ever felt any need to go to hard type tyre has been on my own home track in Summer where it has hard base but soft powder on top.
Tyre pressure: about 12 PSI, I don't guage them but press firmly with my palm, looking for a hard tennis ball sort of feel, tending towards higher pressures these days, maybe drop if it's slop to ride on, or failing that park it up & watch the pigs wallow.
Those S12's wear really well too, I got about 3 seasons out of it, I'd look at it & just couldn't justify changing it. I change the front when it washes out one too many times & I've busted a clutch lever - I hate that.
If you are a real CZ freak, Mitas bought out Barrum, so now you can still have the pedigree.
I'll also add that I'm less & less competitive as time goes by, guess it just doesn't matter anymore, aint never gonna be a champ nor want it.
It always amazes me when I see (usually a newbie) turn up with crap tyres & look in dispair as he smokes me around a corner, I must be under estimating the available traction but then I also hate falling off. Thats why I use good tyres.