I'm going to label this a pending success. It doesn't leak but until I hook it up to the pump and take the system on a dry (well technically wet) run I'm not going to give it the final stamp of approval.
You'll gather from these pics that I am by no means an expert in metalworking. In fact, this is my first go at anything like this besides soldering speaker wires. Thankfully my dad has 60 years of engineering experience and all the tools I needed to pull this off, although this was out of his wheelhouse as well.
Thoroughly cleaned and being heated:
Closed the hole as much as possible. Cleaned and fluxed:
Soldered the hole closed:
Clipped the wings off of that clamp:
Filed the edges, cleaned and fluxed the patch:
Skipping the two failed attempts and getting it to stay on... here is the final product. You can tell by the excessive solder that it was a bit of a challenge for us:
And that's that. $0.20 plus some flux and solder and the $170 coil is not leaking anymore.
Side note: I found out on a thread here about soaking copper in star san... holy crap, the results are incredible. Just compare these pics to the first post.