[captainclock1988]

One way to repair a broken wire on a coil is to take a copper strand out of some 18 gauge electrical cord, make a "J" hook or loop, make a splice, and solder the remaining coil wire to it in the hook, and reattach the other end of the new copper strand to the terminal. You could really use anything for this, such as 20 or 22 gauge solid wire, within reason, as it's easier to work with. If you don't have steady hands, or eyes, find someone who does. Antenna coils are pretty forgiving, you can often unwind six inches or more off of them to re-attach the coil to a terminal, and it doesn't detune them, though if the end that is buried under the coil this is where splicing on a pigtail comes in. Some really brave people actually rewind damaged coils, or even output transformers, but there are maths involved unless you can measure how many feet of wire was used on the original.
I don't think that sulfur in the wax is the issue, at least not in Philco sets, the problem there was nitrate based celluloid used as an insulator, the nitric acid leaches out sometimes and corrodes the wire, usually on the primaries of RF coils, though the police band coils in model 60s suffer from this as well, the secondaries are usually fine, and for some reason are on the coil form itself.
Regards
Arran

Howdy, I agree I believe what caused this wired to corrode was most likely what you said was the insulation on the wire, because when I attempted to "strip" the wire so I could  attempt to resolder the wires back together there was what appeared to be some paper like insulation under the enamel coating. Thankfully the break in the coil was near where the wire went to the terminal and soldered into the terminal so its only about a 1/4" of wire I would need to make the repair you are suggesting, and I do have some small gauge magnet wire that I got in a box of stuff that came from my great-grandfather so I think I could use that to try and make the repair you suggested. 
I wonder if radios from the 1930s in general had issues with bad coils where they had breaks in their coil windings due to corrosion because this is the second radio from the 1930s that I've worked on that had damaged coils due to corrosion.