[Arran]

Hi;
  You do have a radio-phonograph combo of a very interesting design, and I think that you are correct about the purpose of the convertor box, have you removed it and opened it up? Most of those I have seen are for operating radios from 6 volt storage batteries, not converting DC mains to AC for an AC motor, though I have heard of such units. You could probably eliminate it, assuming that the motor on the record player is a normal 117 volt, 60 cycle, shade pole type, however that would not help you as the mains frequency is probably 50 cps where you are, so the motor would spin at a slower speed. I have a set of Riders manuals, but they probably won't show you anything that you don't already have, still I will see what they have on these sets if you can wait a day or two.
Regards
Arran