The problem arises because the plate is too thin. It's possible to correct it and I'll suggest you two ways.
1) The easier way.
Gouge the circumferential welds by the same side where the draw is. If it's inward, as you say, then it means that you'll have to gouge the welds from the inside of the tank. Attention though!!! If you use a carbon electrode for gouging, you'll have to remove thoroughly the discolorations produced by gouging, because that discoloration is a carbon rich region, where the corrosion resistance will be sharply reduced.
If you use a grinding disk for gouging or for cleaning the discolorations, attention!!! In this case, the disk must not be made of silicon carbide (carborundum) for the same reason explained above. The disk should be made of alumina. Once the welds are gouged, weld them by the same side where the gouging is. The warpage should disappear.
If not, you'll have to go to the second (and more difficult) method. This I'll explain you if, after you've tried the first one, you've got poor results.
Giovanni S. Crisi
Sao Paulo - Brazil

Bruce,

I believe the answer to your problem is modifying your welding plan.

Since the section thicknesses are fairly light, I would fit up the welds with a root gap of 1/8" to 3/16". I will make an assumption that your are welding on rollers so if not, let me know. Purchase ceramic backing material(I like the Refract-e-back by alloy rods).These tiles are 1" square and come either flat or with a groove to mold the weld bead opposite side. They come in strips with a foil tape and adhesive to hold them in place. Assure that the surface to mount them is clean and free of any dirt or oil. Apply the backing centered on the weld fitup on the outside of the tank and weld from the inside. Once complete remove and clean the out side and touch up any questionable areas. Make sure this complies with your Welding Program Procedures. I am confident that this will minimize the problems you are having. I would run a few samples with this technique to get a good feel for it as you may wish to adjust the root gap to suit your personal style.

I have found that the extra cost (about 2$ a foot) is more than offset by the savings in labor and the quality of the finished product. Good luck with your project.

Steve Dodd