Progress report - It all worked, and so much smoother than I first thought it would be.

I still need to work on how to keep the pre-melted solder somewhat respectable instead of flowing everywhere, but I've got a couple of ideas for that.
Also surprised that the stainless rod is such a bad heat conductor that I could hold it in place by hand (the other end of the rod) while soldering.

Thank you all so much. This has been a real learning experience.
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