[Arran]

In looking at the schematic it does not seem possible for the radio to work with an open field coil on the speaker as the speaker field acts as the filter choke for the power supply, without it most of the tubes will not get any plate or screen grid voltage. If the radio works and the tubes are all getting plate voltage then the problem must lie elsewhere. Now what else could be wrong with the speaker? Well it could be an open output transformer on the speaker, in which case the 6K6 tubes will not be getting any plate voltage, to one or both 6K6 tubes. The voice coil could be open but that seems unlikely, if it is open then it would have to be a mechanical break in the connection to that coil. Now the speaker voice coil could be stuck due to a warped cone, that often happens if the radio is store in a damp location; it can be repaired by shimming between the voice coil and the pole piece and wetting the cone and spider to realign things.
What exactly does this set do when you power it up? How does it behave? Have you gone through the set with a volt meter and an Ohm meter to check the resistances, continuities, and voltages of coils, transformers, resistors, and tube pins? You really should rule everything else out first before concluding that a hard to find part needs to be replaced.
Regards
Arran