Don't they sell enamel hardeners that work with alkyd enamels? I thought I remember seeing some once that was meant to be used with oil based implement paint or something. I can't recall exactly what it was though.
It all depends, there are all different levels of alkyd paints, some are modified with acrcylic resins and call for a hardener. It all depends on what the manufacture states on their TDS sheets.
Rustoleum doesn't make a hardener for it's product. Without the urethane resins to kick off with the hardener all that was accomplished was adding a can of something that never dries into the paint. You need the both the hardener and the same resins present for the chemical reaction to happen