I appreciate the warning, but, for better or worse, I silver soldered it yesterday.
Luckily, everything survived, but it did take me a couple of hours to sand solder off of places where it didn't belong. Unfortunately, one flux is flowing, the solder is sure to follow it.
I totally agree that I was trying to peen down too much material. That is a lesson learned for next time. This was the first time I did this peening operation, and I just didn't know how much was too much.
I really wish I had someone with experience looking over my shoulder as I do this, saying, "You might not want to do that..." before I actually make a dumb move.
Thanks for the advice. I appreciate it.