Is it possible to bend something to a closed shape? The parts I'm working with are made from 2x1x.125 steel box tubing.

Using a brake (is there one that can handle short lengths (6" or less) of .125 or .093" mild steel?), I figured make the first 90 deg, slide the sheet out an inch, make the next 90, slide it out 2", make a 90, and slide it out the last inch to make the final bend, to as far as the fingers will allow (60 degrees?). Then clamp the part in the bench vise or shop press to close it, and weld.

Currently I'm taking lengths of the box tubing, scribing them, cutting out the corner notches with a saw, bending them (into a roughly M shape /-\_/ ), and TIG welding the open seams closed to keep the shape. It's taking way too long, and I'd like to have this part fabricated by a sheetmetal shop, where the flat can get punched or laser cut, and then bent to shape. Qty would probably be batches of 20 a few times a year, and it takes 2 days to do one batch now. The bend radius must be very tight (2" to centerline), which is why I have the mitered corners, instead of using the tubing bender. Thoughts?