Abrading the stainless under an oxide cover of oil can get it clean enough to solder. You see, the problem with stainless is it contains chromium. And nickel, I think. The chromium oxides are really tough to dissolve, but if you remove them mechanically and don't allow air to contact the cleaned surface, the bare metal will take solder.
I haven't tried this on stainless or aluminum. It was recommeded here for aluminum, which is worse than stainless to solder.
Try an automotive AA cell powered paint chip grinder or a Dremel with a rubber abrasive (Cratex etc) tip.
Doug Goncz Replikon Research Falls Church, VA 22044-0394