I was going to cut the top after the cage install but it is going to be much easier/cheaper to cut the top first, that way the section that drops down is not effecting the design, I would not cut the top until right before the cage goes in, not sure if it would settle or not but no point in driving it or encouraging it to sag in any way.
Disclaimer: It shouldn't cave in two unless you just kept on cutting through the floor and frame. /forums/images/graemlins/eek.gif
Before you bolt down the cage/frame tie in, just jack the body up until the doors shut the way you want them to.