I honestly dont see how welding an 1/8" thick piece to some 14guage floor pan material thats flimsy is going to stiffen anything up. I can only see it tearing there if its 2 or 3" long. If I was going to tie it up to the floor pan, Id cut the rear section that floor pan level, and seam weld it inside the car. Ill have to do that when I have the interior out of the car when I redo the seats and headlinner.

Kasey