Maybe your future son-in-law has a gas welder you can use for this... I wonder if changing the thickness for the flux core wire would allow you to reduce the heat going into the metal. Another thing you can try to do is make a heat sink of out of copper, I beat a copper pipe into a flat section that i clamp to the back of the metal, this allows some of the heat to be absorbed into the copper.
How much more welding do you have left? I assume the rest of the car? Might be worth while to pickup a gas-compatible welder. Checkout the panels after i ground them down, I used a finger sander from harbor freight, great for the tight spots.
Also imma just say it now, **** Airgas, go to a Praxair, or even better a mom and pop shop. My local Airgas has a bunch of shady sales people, overcharging for gas.
This 80 CFM tank should get you around 4 hours of trigger time, https://store.cyberweld.com/shielgascyl8.html the refill for me is ~60-70 bucks at Praxair, I bought the tank locally because I dont want praxair to go out of business and ill be stuck with airgas.... That cyberweld tank with the fill is probably the cheapest thing you'll find, but call local and see... if you do go down that route.