I would usually cut the frame before it rises for the rear axle clearance. Where to cut depends on where various body mounts are. I would also tack in a metal brace between the frame rails on the portion that will stay with the body so the frame wont move. Doesn't have to be anything huge, and some 1.2"-2" angle tacked in will keep things located so they don't spring when you cut behind to remove the back half.
Then once the back frame is removed I would build a crossmember to span the frame rails, and weld it in permanently. After that the brace can be removed. This crossmember will be what you attach your narrowed frame back half to when it's done.
This is a picture of my buddy's old '37 Plymouth coupe's frame where he back halfed it for monster tires and wheels. You can see how they built a crossmember, then narrowed the rails and reattched them. The body is still off, so I can get some other pictures if you need any further looks:
If you're going to keep the car lower, then you'll need a offset in the crossmember to give driveline clearance. His car is a gasser style, so no offset needed in the center for driveline clearance.