seating m-14 mags
If the empty mags fit, and the full ones dont, then the loaded rounds are causing your problem.
Pull the bolt back and lock it to the rear. Then insert the loaded mag. It will probably go. If the mag was modified by sticking five rounds in it, then pinning it, the follower does not go down quite far enough.. With the bolt closed, there is not enough room for the rounds to go down in the magazine when compressed by the bottom of the bolt. If you take one round out, they should seat, because you have then given them clearance.
Also, when seating the mag in the m-14, you should insert it at an angle so the front is higher and can catch on the front slot. Then, you pull the magazine back and up until it clicks into place. Sort of a rocking motion.