Williams engines and RailKing transformers

For almost 20 years I've run various Williams and Williams by Bachmann diesels and GG1's without any issues with MTH Z500 (50 watt) , Z750 (75 watt) and Z1000 (100 watt) transformers.

I'm inclined to doubt that the problems are transformer related.  These are standard AC locos and the MTH transformers are pretty much standard modern transformers.  Not sure what AM and FM means to your expert commentator, except as metaphor.  It's true that postwar Lionel transformers did not use pulse power, and the new ones from MTH and Lionel do, but  this factor shouldn't lead to overheating or failure in most uses.

Almost sounds like the motors are drawing too many amps.  Have you cleaned and lubed the gears?

I have not had any problems running my Williams engines with an MTH Z-1000 transformer.

Regarding "AM" and "FM" these terms were not explained. I do not know what they signify.

FWIW, I find that some of the motors that are in Williams stuff seem to run a bit hotter than Lionel or MTH.  Not absurdly hot, but they seem to draw more current with no load at a specific voltage than the other brands.  Most of the motors that I'm seeing with this characteristic have no model nomenclature, so I have no idea what brand or model they are.  The ones I am comparing them to are usually Mabuchi motors.