minangelo,
My $0.02 worth,
If I were trouble-shooting this fault,
I'd be looking at the Step-down Transformer itself, it sounds like there may be an internal connection problem, possibly where the HV or LV connections come through the Bushing on the Transformer body.
BTW, when the lights dim, did you notice any particular noises coming from the pole wiring or the Xformer, like a buzzing sound?.