The stiffness of a piece of silver solder is no reflection on its'composition.
A rod directly extrudes to size is softer than one produced by spin-straightening a hard drawn wire!
1) Cut a small piece of your strip to a similar size to that you can make from your 1.0mm 55% cadmium free rod.
2) Place both pieces on a small sheet/strip of copper and apply flux paste.
3) Heat the two pieces eveny from underneath.
4) Observe when the two samples melt.
My bet is that the unknown material will melt just earlier than the known. It may even spread a little further!
My bet is that you have a 42%silver alloy with cadmium. 5 x 1 strip was commonly supplied to shipyards and the automotive industries. One way you could put down metal slowly. Turn it through 90 degrees and you had a thick rod and could put a lot down quickly
For the alloy to become so tarnished implies that it has been lying around a while. This may date it before anyone became concerned about the health risks for the model engineer of using such small amounts of silver solder.
All my other thoughts on original source etc stay with me!
Keith