I actually welded the extra strip in place. I drilled the box section at intervals between the places where I was going to drill for rail hold-down bolts, used a wooden wedge arrangement to slide down the box section to hold the strip against the inside of the box, and then welded to the strip through the holes. Bit of grinding to clean up the outer surface of the weld and job done. Other people have used Gorilla Glue to fix the strip in place - it only needs to hold while you are drilling and tapping and then until you bolt in the final item. Your idea of welding at the ends and then working along, bolting as you go, would work as long as the strip does not sag too far when you take the bolts out to fix the final item in place. In the case of my long rail supports, these are 1800mm and would have needed fixing at more than just the ends.