Aligning the rims on a functioning mosin is not ever needed because of the interrupter.
I would check 2 things on this rifle. First, replacing the interrupter is easy and cheap - you can find them on ebay for about $10. It may also be that you need to clean the existing interrupter as dried cosmoline may be causing some problems.
If the last round were the problem, I would also check the angle of the follower - I have fixed several mosin feeding problems by bending the follower slightly.