Really hard to tell from your description.

I rank the Carcano safety only slightly better than the Mosin Nagant and I'm not sure I wouldn't switch that view fairly easily.

I just went up and worked the safety on three different Carcanos. I don't think I replicated what you describe with any. All three lift the bolt up when you try to put the safety on so it is a two handed operation. One to move the safety, the other to hold the bolt. All three have a very strong spring that hold the firing mechanism back so not sure how yours is releasing forward. Two functioned fine. Pull the trigger nothing happens. Return the safety to fire and they fire. The third is a real pain to get back off. Nothing clicks or moves when the trigger is pulled but the safety just wants to be cantankerous and not move forward and back to the right until I manipulate the bolt just right.

If I were to hazard a guess, the spring on the safety may not be strong enough to hold the firing mechanism back. Since you have two bolts, try swapping the spring from the other and see if that solves the issue.