You're going to need something a lot bigger, and with gas. Especially with the difference in thickness between the different metals. Welding the Bad Dog to Zed pans isn't that bad, but when you go to weld the Bad Dog to the original metal, you are going to have some serious problems blowing straight through the original metal, and it's going to be a complete mess, even if you manage some control.
You don't necessarily need an expensive MIG, I did the project with a cheap old 110V "Migmate", but with gas. I had to practice a LOT with the different welds, upside down, and between different metals, joining different ways... I would suggest you do the same. Even after I got comfortable, I ended up going back over most of the welds again using a different stitch pattern to try to get more coverage to connect the metals better. If you use flux core, you are going to bust straight through the thin metal and leave splatter everywhere. It's going to look like you popcorn-ceiling'd your car.