+1 on not doing any metal removal until the rivets are in. Things will probably shift a little. Having said that, it is a good idea to check the fit up as soon as possible. I like to check it before I press the barrel out. That is a good time to confirm that the piston is going to line up with the gas port. If the receiver or trunion is out of tolerance, the problem will be magnified at the piston. Sometimes that it will cause binding. Also, if you try to shift the position of the trunnion in the receiver, you may throw the piston out of alignment.
Since you have a press, and you have advanced warning that everything is not perfect, I would press the barrel nearly all the way back in and recheck the alignment. If the piston lines up OK, then the receiver is not warped. If you can shift things so that the rails line up and the piston still lines up, then all you have to do is figure out a way to make sure it stays that way while you rivet (not easy). If you cant get things to line up OK, come back for more instructions.
I don’t mean to make this sound like a major big scary problem. It is just that you are smart to bring it up now, because now is a good time to scope it out. Chances are, everything is going to turn out OK. AKs will tolerate some misalignment. The tight carrier may just require a little rail filing after things are together. You may also need to twist the receiver or tweek the rails, again, after riveting. Don’t worry, I (and I am sure others) have survived both of these problems.