Short version of long story. When I was installing 5.13 gears in a converted Sammy rear differential housing, I had to pound out the step in the back of the housing to get it to fit.
You can see the step in this photo

And this is what it looks like after pounding the step out

If you are installing 5.13/5.12 gears in a Sammy, you will need to get a "Can" to hold the pins in place, or tack them so they can't come out.