I agree your mystery solder is probably something that works in the 375/400F range.
The cadium solder on the loops is probably a 900F+ hard solder. Again just guessing, but anything in the 200/250 range would be one of the bismuth alloys or the like. Those generally are specially solders used for emergency repairs. Not a lot of strength but easy to use with nothing more than quick heat of a match or lighter.
Cerrosafe alloy for chamber castings and backing up items to be engraved is one of those low temp melt alloys,,melts in boiling water.
I'd try the mystery solder out. It's probably 60/40 or 50/50 alloy lead/tin mix. It was and still is sold both rosin core and solid wire..
Common solder,,till all of a sudden it needed to be pure tin mixed with a couple % silver or it'll fall to pieces,, or so we're told.
Millions of bbl ribs on SxS guns, underribs, top ribs, sights and swivel bases were and are attached with nothing but lead/tin solder and have held just fine for centurys.
It's the solder job,,not the amt of solder that does it.
Use an extra flux. The rosin flux in the wire isn't enough for the job. Common No-Corrode paste is fine. I've re-ribbed countless SxS guns with nothing more, everything from Stevens to Parker to Purdey.
If it really bothers you,,dump it into the bullet melting pot and buy a roll of new solder and be done with it.