Your soldering iron puts out a strong AC field. That radiated field what is getting into the transformers. You might want to double check that the drain wires that connect from each transformer to the safety ground have been well connected to the safety ground screw, and that the insulators under the all transformers are properly installed to insulate the transformer from the chassis. If they are not there is the possibility that the radiated field from the power transformer (which is, by design, a very small magnitude for a transformer of this size) is getting into the output transformers via eddy currents generated in the chassis panel and up thru any mounting screws that are not isolated from the chassis.