I would agree on the long passes with MIG as that would be close to impossible, but with the TIG or O/A gas welding, a full weld pass with no gaps should eliminate much of the distortion realized providing the panels were tacked first to hold things.. Of course, all this assumes weld placement in a good panel is not in the flat low crown area of a door, etc. There's no shape there to help hold things, and things ARE going to move. Weld placement should be based on accessibility for planishing and panel details to help hold things from getting carried away (bend lines, bead details, etc)

We'll video the next step after tacking this evening..