Mike,
Door welding sucks. There is absolutely nothing supporting a vast expanse of nearly flat, thin sheet metal.
One thing which may add to your type of problem is the length of time spend creating each of the tiny little welds. A common error is have the power set too low, which requires one to keep the button pushed longer, making more heat. The little weld needs to be a quick buzz and you are done.
Have an air hose handy to blow air on the surrounding metal (not the weld) to stop the heat from migrating to the rest of the panel. Lightly tapping the surrounding metal (not the weld) will also stabilize the structure of the metal on a microscopic level. The molecules are in a state of flux when heated. The tapping helps stabilize this flux.
