[Arran]

I don't think that the phase (not polarity) of the field coil winding is a factor, it's what they call "bulk wound" and it's two main purposes are as a choke, and as an electromagnet, and has 100s of turns going from right to left, and back again. The hum bucker (some schematics mark it as Hum Neut coil) is normally connected in series with the voice coil, but out of phase with it, not every field coil speaker has one though, it looks like the Philco 42-380 does not, although it may have but may have been left off the diagram. If there is minimum hum at low volume I think that the hum bucker is connected correctly, the hum at high volume is likely coming from the audio amp itself and not the power supply.
Regards
Arran