Here's what I ended up trying.

I cut thin strips of masking tape and taped the pin/clutch back to the key (steel BTW). Then I used my gun to heat up both parts. I broke off a bit of solder the length of the pin back and wedged it into each side and heated them up again.

Didn't look pretty, but after it cooled I took off the tape and it held in place fairly solidly.

James: I could mail you both keys and a few backs if you wanna fix them up and you could keep one as payment.