Another thought, and if someone who knows more about this wants to chime in, or even correct me, I'm all ears: Silver solder. The melting point is a higher, but I have the idea it makes a MUCH stronger joint than does conventional solder. Enough so that--this really surprised me--even BANDSAW blades can be rejoined successfully using only silver solder.
I'm posting this one just to show how strong silver solder joints can be. I THINK they can make a smaller joint a lot stronger, but using a lot less solder (I'd try the smallest diameter I could find and work upward as required)
I also recall resistance soldering tools can make smaller joints than other methods, but even using high heat, like you might get using a propane torch.