Fixing the burnt breaker was *much* easier than I expected. I decided
to simply remove the breaker entirely from the box; connected the
incoming wires directly to the loads with wire nuts.

Now, before you blanch or jump to reply to such an insanely stupid
action... here is something I didn't know about the system until
yesterday.

This house originally had a fuse box. About four years ago we had the
entire box replaced with a proper breaker box (tired of buying those
d*mn fuses!) It turns out that the electrician fed that little
outdoor box through a 30A breaker in the main panel!

So there were *two* breakers on that circuit, one in the main panel,
one in the outdoor box. I just removed the one in the outdoor box. To
restate: The circuit *has* a 30A 220V breaker, it's in the main panel
and has been for four years.

Again, many thanks to Stuart. Without your suggestion I probably
would not have taken the time to look more closely at the main panel
connection.

Best -- Terry
....who is now overjoyed to be able to rewire his new welder from 120
to 220V...life is good...