Hi Bnw,
I don’t think you’ll be able to hide those welds very well. One of the issues is the new piece you put on sits off the structure you welded to. One cause of that is you welded on the outside of the fold of the original piece (on the left side of your photo) causing a large gap. That made your edge welds that much thicker. It also looks like you are trying to form the metal after it has been welded in. I would suggest forming the piece before hand so if something goes wrong, you only need to make a better piece.
When I make a patch, I start by making a cardboard template.
From there I’ll trace the shape onto a piece of sheet metal. If there are folds involved, I’ll make sure that the fold doesn’t go outside the dimensions of the template. Any folds I didn’t have on the template, I’ll add onto the sheet metal. You can see that where I have the blue contour gauge making a 5/8” fold area.
I’ll also use the cardboard to make a buck for any weird curves that need to be folded. When I cut the plywood, I’ll cut it taking into account the thickness of the metal being folded. Once again, trying not to go outside the template dimensions.
To fold an inner curve like this I started with a round head plastic hammer then moved to a metal hammer to stretch the sheet metal into the final shape. Then it is a series of test fits and adjustments to get the new piece to fit.
Once that is accomplished, drill a bunch of holes spaced 1½”-2” apart along the edges that will be welded to the parent structure. I usually use a drillbit slightly smaller than a ¼”, but a ¼” would be good if your welding onto a thick piece of metal like the frame. Clean all surfaces and clamp the two pieces as tight as possible as you weld. You don’t have to clamp the entire piece all at once, just where you are welding at the time. As you do each plug weld, you may have to use a hammer to flatten any warpage from the heat. You should do this immediately before the metal cools.
If you haven't, practice doing plug welds. There is a learning curve to melting the underlying piece before you cover it up. A bad weld will sometimes "pop" as it cools. The round welds in the last photo were done with a MIG welder. The butt weld on the right was done with Oxy-acetylene.
Hope this helps.