Is the bolt hard to close when there is no round in the chamber? If NO, then the scope base screws are not the issue. If YES then the scope base screws are the problem.
If the bolt closes easily on an empty chamber then the hard bolt closing is related to the ammo. Not all factory ammo is created equally. If it is crap Norinco ball then maybe try something else a bit better quality. Just because "factory" ammo chambers tightly is not an indication of an out of spec chamber.
As long as the bolt closes without excessive effort, it will be fine. Headspace is not a specific measurement, it is a range and it is certainly possible to run into minor issues with a minimum length chamber and maximum length ammo. A minimum headspace chamber is fine as long as it does not require a ton of effort to chamber the round. Even then a short chamber is not dangerous to shoot. It is only considered "unsafe" from the point of view that a live round cannot be removed from the chamber if need be. A minimum length chamber will not cause excessive pressures unless you have to beat the bolt handle down with a hammer.
A long chamber can be dangerous to shoot because it can cause a case head separation or split case during firing which will result in high pressure gases being vented out the back of the rifle into the shooter's face.