I have the same problem with the standard AK sight. I tried replacing the rear sight on my SLR 95 with a peep sight. It was easier to shoot, but I got no better (even a little worse) accuracy. Then I put a peep sight on the rear where it belongs and presto, it is like shooting an AR. My group sizes dropped by half and it is much easier to shoot. The problem is that I havent found a source for rear peep sights. Mine is a Krebs that I got second hand. The last time I checked Krebs wasnt offering them anymore.
There is one other thing that may help. My Saigas are a little easier to shoot than my military AKs. The main difference is that the rear sight notch is wider. The other difference is that the full length sporter style stock makes it easier to get a good cheek weld.