[Arran]

Mike,
This is just a thought, the are on the coil where the verdigris (green oxidation is) I wonder if that is where the break is?? It may be possible, since the coil is not varnished together, to splice the wire back together, from what I understand filed coils are bulk wound, so the direction, and pattern of the turns isn't critical. If you have an empty spool you could unwind the coil onto it, till you find the break, repair it, and then wind it back on, though the bobbin then used doesn't look easy to do this with. This is assuming you want to spend the time repairing the speaker, but it's kind of like repairing an 8 track cartridge, it's sort of like knitting even though you can buy scarves and sweaters from the store.
Regards
Arran