Good find, and glad to hear that you're willing to get down 'n dirty with it!

I'd recommend setting the TIG welder off to the side for a while and get a MIG for the sheet metal work. The TIG can be used if you know what you're doing though: to find out, get a sheet metal shop to sheer up a dozen or so strips of 20 gauge about 12" x 4" and practice butt-welding them with the TIG. I learned to do this a long time ago with gas welding but prefer a MIG.

I don't know what your prior experience welding the thin stuff is but whatever the welding process you use, the big trick is to tack the two strips together first, going slowly enough to allow the metal to cool and the edges to come back together after each tack before moving on to the next at one inch intervals. If you do it right, you'll have the two strips tacked so that they are dead even without warpage. A good sign when using the TIG is being able to tack the two strips without using any filler rod.

Patience is the key; most people get excited and start tacking too fast and warp the metal. The five minutes that you take to tack the strips together seems like a long time but is nothing compared to the time and skill needed to fix warped pieces. Add tacks between all the first tacks, then another set after that. That should set you up for the last step.

Finally, the welding can commence, with the same slow pace for the same good reason. The welds should be about the size of two tacks to keep the warpage down. Some people recommend hopping around when stitching the panels together but I go from one end to the other, again letting each weld cool and making sure the edges are staying level. If things start to get out of line, stop and hammer them lightly back into position, then continue.

Expect to spend an hour each on the first few strips. Tedious but well worth the time, as straightening a warped panel after someone has rushed a patch can take two or three times as long.

I use a MIG as that keeps the temp down but requires grinding after and isn't as easy to correct edge misalignment as you go. If things need to be hammered, the tacks need to be ground flat first. I find using a MIG also reduces the time needed to do a patch by a fair amount.