[Arran]

That's curious, I didn't notice that the #45s and the other tubes shared the same filament winding, most of the late 20s early 30s sets have separate windings for the power output tubes. So yes that is what the wire wound across the winding is for, hum balancing on the #45s, which isn't needed fore the rest of the tubes since they are indirectly heated. I believe that the resistor connected between the tap on that hum balance resistor and ground is for biasing purposes, to make the filaments less negative with respect to the grids, it's at one end of the long voltage divider resistor.
It's a good thing that they chose to use a tubular style enameled wire wound for the voltage divider, it's probably why all sections of it still read good. If it were a candohm type riveted to the chassis you would be mixing and matching modern standard valued power resistors trying to make a substitute.
Regards
Arran