I have never been able to shoot the Browning BPS shotgun because it just dose not fit me, which is a drag since I shoot shoulder guns left handed and I liked the ambidexterity it affords, much like the Ithaca 37, which I love to shoot.
In your situation i would suggest shooting a box or two through it if possible and then consider a thickened recoil pad or spacer for the LOP and considering having it modified to fit. As for the drop, a good carpenter could raise that for you. A lot of messing around to get it right in my opinion.
In stock fitting 1/8" can seem like a mile....
