Not only does stainless steel foil not cut well, stainless steel plates do not solder well with basic lead-tin solder. resin flux, and a cheapo 25 watt iron.
From the Internet, I have learned that you either need hydrochloric acid, or silver based solder and a much higher wattage iron or even a torch. I don't like using or keeping dangerous chemicals, and HCl is fairly high up in the danger scale.
I attempted to use a butane lighter to heat the stainless steel which I had sanded/roughed after my first failed attempt with an iron. The lead solder formed a ball and slid around on the surface of the plate, resembling mercury. It refused to bond, however.
This is for a probe attachment for my CNC. I've decided to skip the soldering, I will just bend at right angle in a new strip of stainless, and drill a screw hole and attach a lead wire to the screw.