Bye, bye, dent!
I surely made some mistakes. I don't even know if I went about any of this the right way. But the end result will do for Trail 90 purposes.
There wasn't a single cathartic "pop" as I hammered through from the back side (which is kind of how my naive self imagined it'd go), but I was able to slowly work the dent out.
The arm is straight now, too.
Before I tried welding up the punch holes I practiced on scrap 16 gauge sheet using short lengths of round rod as filler. After a half dozen attempts it was going pretty well, so I cut a piece of rod flush with the surface of the first hole, struck an arc, and INSTANTLY blew through the swingarm. Whoops. I'm not sure what I did wrong, but I turned down the amps and eventually got it patched up.
I also welded the seam near the axle, which separated either as the result of my work or when the farm kids initially bent it out of shape. That went surprisingly easily so it was a nice to end on.
Then I filled in my handiwork. It's more-or-less as smooth as the rest of the machine, which is to say, adequate for a rescue Trail 90.
I still have to decide what to do about the broken buddy peg mounts, but I'm anxious to move to another part of the bike for now.
I have to say, every time I create chaos with my little welder it really makes me appreciate all the amazing work I see everyone else posting here.