Hello charlie128, the description is a bit vague to provide answers for you. If you could include photos that would be a great benefit for everyone on the forum to look over and make suggestions from.
     From what you have stated I would possibly try to suggest clamping heat sinks of some sort on the back side of the doors and fixturing of some sort to restrain the material on each side of these stiffners as well. Copper would be preferred, but aluminum would likely work too. A bit more information on the heat sink/restraints combination that I am referring too: the heat sink piece should be large enough to be able to center it on the backside of the area to be welded, the restraints should be designed so that they can be positioned on either side of the stiffner or clip that you will be welding on and then clamped into place. Additionally, it is often beneficial for these restraints to be fairly thick and have a bevelled edge that is oriented close to the place where the welding needs to take place, the bevel will allow for nozzle access in the area where the welding is taking place and at the same time aid with distortion control. Instead of setting your welder to a lower setting, consider running a bit hotter and faster, this may help to minimize the arc time and thus the overall heat input which could be contributing to excessive distortion. A bit for you to ponder. Good luck and best regards, Allan

If I have a correct "minds eye" vision of your problem-----  All welding, where heat is involved, will produce shrinkage, distortion and some sort of grain growth discontinuities that may be objectionable for architectural appearance purposes.
First;  "Gloss Paint" is the world's greatest welding inspector, and the greatest architectural critic.
Second;  I think the best thing you can do for architectural appearance is to redesign the part to allow "snap welded" studs as fasteners for your stiffeners or to simply spot weld the pieces on.  The spot welds can also show through, but snap welded studs can be made that will have no telegraphing through the part if the nuts are not tightened too much.

All great replies, so I only have one thing to add to what has been said thus far.

Find and purchase a copy of John P. Stewart's "Flame Straightening Technology for Welders" for your personal library.

This book also gives desgn tips and examples of fixturing to prevent warpage, techniques to use while welding to prevent or minimize warpage and distortion, and also examples of how to straighten welded items after they have been pulled out of shape by the heat from welding/cutting, etc.

The ISBN# in my copy is 0-9692845-1-9