Standing on the shy side of 5'4" and before the midlife weight gain hit I was 125 lbs. so I can take an educated guess on your problem. You didn't mention anything about having the LOP reduced to fit you. The fact that the Moisin doesn't give you as much issue is part of the give away to your issue.
Moisin's have a shorter LOP than a FAL 13.5" vs. 14.25"....that 3/4" makes a huge difference in how you end up holding the gun. This is forcing you to lean too far back and hold your other arm out more to hold up the weight of the gun. This stretching is putting you off balance and exacerbates the recoil. For me, I prefer about a 13"-13.25" LOP. Get measured by a smith and have the stock shortened to fit you; it will make a world of difference.