When I was a kid, I can remember that some households had a special
sleeve ironing board (although they were made of wood). With those ironing boards. it was gravity that kept the material flat against the board or platen. In your case, how about letting atmospheric pressure help .....
My idea would be to make a fixture with a vacuum platen along the same lines as the sleeve ironing board - i.e. cantilevered so the pipe can be slid over. Not sure exactly what scale would fit, but have, say a 4 inch wide platen, with a 1 inch blank strip down the middle as the 'anvil' and then a 1 inch wide strip either side drilled with lots of small holes (*) down into a channel which is running through the platen, from which you draw a vacuum. This way you have no impedimentia on the top surface leaving access completely clear for the welder (**).
I'm not sure what your welding process requires, but having a flat top to the platen would mean the edges would be butted square to each other, alternatively having a slight crown to the platen would present the work with a slight V between the edges. If the welding process works best with a backing plate then leave the central strip of the platen flat; if it produces any sort of bead on the back then you could machine a relief groove down the centre of the platen.
To help with loading, you could make the platen so that the two sides each had their own vacuum line and you could then open one side and place one edge, then fold the other one over and then open its line. Would suggest you provide some proportional valving so you could clamp enough to align then hit it with full vacuum prior to starting bending/welding. Depending on how many pair(s) of hands are available to load the fixture, you may find it useful to provide foot-pedal control of solenoid valving.
To get the first edge aligned with the centre of the platen, you could have a few drop-in or pop-up stops or dowels or similar arranged off-centre so that when the first sheet was butted up against them then its edge would be on-centre; then pop the stops out of the way to clear the way for the second edge. If the stops were pop-up with just had a weak spring then you might be able to leave them in place and let the second sheet just press them out of the way (or if you wanted to be really clever make the stops as tiny pistons that were sucked down when you applied vacuum to the second side....)
You could make the fixture as long as your max length and then just throw a rubber blanket over the un-used portion.
(*) vacuum holes - I'd machine them as, say, 4mm pockets 4mm deep with a 1mm drilling down into the vacuum. The vacuum chamber beneath, rather than a tube could be a slot milled into the base of the platen which was then sealed with a plate. I might also be inclined to look at segregating the length into several zones and providing each with a decent diameter line back to the vacuum set. You could also provide a suitably two-way-valved arrangement to allow you to blow-down with compressed air if you needed to clear the holes occaisionally.
(**) because of the open access this will provide, it could also be possible to have rail(s) above with a trolley on for the welder to run the gun/torch on to keep height/line.
Dave