I have found that on a badly rusted relic that no matter how well you think you have cleaned it there will always be pockets of insidious rust that may not be visible on the surface. Typically they can be found under the dark or black spots. I believe that you level the playing field against this cancer if you bake the iron relic for at least an hour before letting it cool down and applying whatever rust converter you choose. Moisture is one of the catalyst for oxidation and baking it will ensure that even the pockets are dry. My wife does not share my enthusiasm for iron relics so rather than use her oven I bake mine on a hot plate in the garage.
Everyone has their favorites for rust converters. Mine is Ospho.