I drilled the hole with a #10 drill bit until it just broke through the other side. The flange isn't as big on the thread side, so I ended up with half a hole, which was fine (as I only needed to fill solder from that side). I used a small needle file to deburr the hole.
Then I stripped the wire, and tinned it. Then, using a big ass soldering iron (seriously... The thing is like a foot long, and the tip is easily 1/2" diameter) I heated the wire & element flange from the back side, until it was hot enough to fill with solder.
It took a while to heat up. I was originally using a regular sized soldering iron, which would've taken all night. So I grabbed the big one, which took 5 minutes. I kinda blobbed too much solder on, so I had to use a heated solder sucker to clean it up some(An advantage of being an airline mechanic is the access to all kinds of useful tools).
After it had cooled, I cleaned up the gasket flange the rest of the way with a file. Now I just have to pot the PVC coupling with JBweld.
Much easier than I thought it would be.