[Arran]

Jayce;
  Often you can repair the short between field coil and the basket, it may be as simple as a break in the insulation of one of the leads going to the field coil or the primary of the output transformer (if it's mounted on the speaker). This is likely what it is since the field coils are usually wound on a cardboard bobbin like a transformer. Also may of those earlier electrodynamic speakers are bolted together so you can remove the bracket holding the pole piece, field coil, and hum bucker from the basket. On some, like the Philco speakers, they are mostly welded together, but you can get at the filed coil by pressing out the pole piece, this is something I have not tried but others on the phorum have. Barring repairing the short circuit itself you could try isolating the speaker from the mounting bolts through rubber grommets, or by mounting the speaker on a wooden spacer, and then mount the spacer to the cabinet bolts. 
Regards
Arran