Thanks for the advice!
I ended up doing a little filing - now it goes in with a nice, satisfying click. I hadn't had that problem with my other Saiga - a 7.62. I think I'm going to leave mine as is, too, at least for now. My only two complaints now are minor - I'm not crazy about the cheap feeling stocks and I wish the sling swivels were bigger, so a standard AK sling would fit through them more readily.
Still, I like these rifles - great bargain, very reliable, plenty accurate enough for plinking or HD.