[Arran]

The vertical mounted coil on top of the chassis may be repairable, or could at least be rewound if you can figure out how many turns of what gauge wire to use, but there is usually more to it then that. The second horizontally mounted coil is pretty much at the EOL stage, it's been chewed to death by rats and must be replaced. The form will have to be made out of some tubing of the same dimensions, new terminals can be riveted onto the tube.
The Silvertone model 45 may be rare, but that does not mean that the contract manufacturer did not produce sets of it's own using the same chassis, or at least sets using a similar front end. It will take some research but this will probably be the best hope for repairing this set.
Regards
Arran