before going further do yourself a favor and get the old surfaces down to bare clean shiny steel on the front AND back sides. otherwise you are bringing in contaminants to your weld and it will pop and sputter and leave porosity in the weld.
spot weld, all over the place, like G&R is saying. like simply a spot of weld and move on to a cool spot. if you wanted to you could spot and then quickly hammer on dolly to expand the hot weld before it cools and shrinks leaving a distorted panel. spot here and there all over and ensure the panel isn't heating up as you go. it's good to have something else to do at the same time so you don't try and hurry the process. a hurried job will likely cost you more time later when it comes time to get it straight. hot spots in the panels shrink when they cool.
maybe try a smaller gauge wire if possible. I find larger wire tends to weld cooler, sputter more and not get a good penetration. there is also a wire that is better for bodywork because it cools softer so less brittle. not sure about the wire feeder style though. are you talking about what looks like a mig welder but no gas? like a flux core welder? pics?
an auto darkening helmet is also a good to have thing, like c clamp vice grips, magnets (they do, however, distort the weld if trying to weld right next to the magnet. they work good to hold panels in other spots than the weld area) long vice grip c clamp pliers, a wire cutter to keep a chisel tip on the wire so it starts the arc right away, small disc grinder with flap disc assortment, die grinder, sheet metal welding clamps to hold the panels together, cleco fasteners. I could go on. it all costs bucks though. I have assembled my collection over many years. wouldda been nice to have it all back in the day though. I have done lots of sheet metal and body work with literally nothing for tools except whats laying around. claw hammer, chunk of steel, old car parts made to be a dolly, etc.
check this out, maybe some hints here.
https://www.musclecarrestorations.co...eet-metal.html
you could try turning the amps up a bit or travelling slower so you get penetration and not such a cold weld (it just looks cold to me, maybe it is penetrated? no back side pics yet). do you have some pics of the back side? you can also use a heat sink on the back side. I have some flattened out 2 or 3" copper pipe from a scrap bin at a plumbing shop that i use for that. flat like fully squashed. I have several different ones with different shapes for different projects.
keep the pics coming. you're working through it, soon it will be done.