Pretty much straight forward. When you remove all the soil, or as much as you can, you can snap the rosettes off, or use a serrated knife. Then pot them up. I don't water for a day or three, until the broken area has skinned over with a 'callous'. This will prevent rot from setting in.

Congratulations on your recent bloom! I am sure your orginal pot is crammed to the edge, as these like to be very snug in their pot before they bloom.

These can be so top heavy, when repotting I use rocks (on the surface of the soil) to prop the plant up, and keep it where I want it. Once the roots start to grow, or the soil settles, or the plant decides its going to stay; what ever it is that happens, I remove the rocks.

I also keep large keel rocks to put in the bottoms of pots to help balance the height of the leaves with some weight in the bottom of a pot. That is trickier, as overpotting sometimes causes the soil to stay too wet too long.

I used to split mine up, as soon as it had another growth head, but I have decided I like the lush look that multiple plants in a pot gives. I now have mine in a 15 inch pot, and no other pots of S. trifaciata sitting around.