That gap should have been non-existent. You want them as absolutely tight as you can get them. More weld to fill in the void, more heat, more shrinking, and nothing to keep it from pulling together as it shrinks. A good pair of OFFSET Wiss or Midwest shears, right and left, would have done a beautiful job of trimming for your patch. Cut the patch to size, scribe onto the quarter, cut out leaving 1/4" extra, then cut the last 1/4" right on the line. Don't use cutoff wheels, the heat introduced is adding distortion before you even get started.
this is a good place for a refresher video..
https://www.youtube.com/watch?v=qAOQfUaRZyw&t=41s
At this point I would suggest grinding down the weld to just above panel surface before planishing (hammer and dolly) to add some stretch back in from the weld shrinking. If you leave all that weld there, you have too much mass to try and stretch.