You can correct this otherwise unavoidable warpage with careful hammer and dolly work, and you can keep the warpage from accumulating in the future by immediately doing the same at each hole you weld closed, before going on to the next one. Here's an explanation that is necessary to understand:

The filler metal goes in very hot, and swollen with the heat. It heats the surrounding metal, and a ring of this metal not only expands due to the heat but softens markedly. The entire unheated panel around the hot spot resists being pushed out by pressure from the hot, expanded portion. Since the red hot part is soft and sort of plastic like putty, and its expansion in the plane of the cold panel is resisted, the soft metal increases in thickness instead. This growth in thickness due to restrained expansion is called "upsetting."

When the hot, plastic, "upset" thicker metal cools down, two effects happen at the same time: it shrinks in all directions at once, and it gains strength and looses its soft plasticity. It soon becomes cold enough to pull strongly inward on the surrounding panel as it continues to cool and shrink and pull some more. This residual inward pull when cold makes the panel warp elastically. The sheet metal that was hot and upset will not have shrunk its thickness quite back to what it was originally. There is a residual upset.

Your remedy is to hammer the upset spot thinner and thereby expand it in the plane of the panel so as to just eliminate the pull created in the cooling process. The unheated panel "wants" to get back to its unwarped shape if it can. Hammer the shrunken, upset portion directly against an appropriately shaped dolly backing. Lots of small blows with a moderately domed hammer face all over the upset spot will thin the upset metal and spread it out, to get rid of the unwanted pull it has. But first grind away any irregular bumps of filler metal so that the dolly fits flush on the opposite side from the side you're hammering.

Some practice on a scrap panel of similar metal thickness is a good idea. Squares of dead flat bare sheet metal, having holes you filled the same way, might be best for practice since you can tell when you have relieved all the shrinkage and warpage. Hammering too much goes on to cause expansion and new warpage. Heating an overly expanded spot red with a gas torch will upset and shrink it again. Bodymen do this in fixing crash damage where stretches occur.

I used to have a 63 Alfa Romeo whose exterior bodywork was all butt welded together, without visible assembly seams. This was probably by gas torch, which is the worst for heating the surrounding sheet metal. I saw the dolly marks on the inside of the weld beads, and solder filler in pits on the outside. Kinda labor-intensive, but the company was in effect union-controlled back then.

Have fun, and good luck. Good song, too!

Charles Greenlaw