I like your website with the built-in links and all. That coil got lunched, didn't it? Hard to tell but if it was just the outer wires, I'd make a careful drawing of the orientation of the coil in the set and where all the wires go, unsolder it, take it out, and try to scope which broken wires go with which ones. But this coil "looks" like it's beyond that.
One thing you could try, then, would be to carefully unwind the broken turns of the coil, keeping the wire, until you get to just one wire coming out of the good part of the coil. Then carefully scrape to bright copper and solder that wire to the broken pieces one after the other and wind back on as neatly as possible. It's important to wind in the same direction as the coil was originally wound. You won't be able to wind like the machine but that's OK. Have a candle going nearby and drip wax on the coil as required to keep it together. Reassemble and it might work. It might require the tuning cap trimmers readjusted to get it to track.
Another fix would be an oscillator coil out of a junked plastic table radio. Someone on the forum might have a junker that he could send you the coil from: I don't have one at present or I would.
If not, AES sells replacement oscillator coils. I don't know which of these would work in your set, but they're cheap and one of them would: I'd get both and tack them in and try them. Search "oscillator coil:" see the first two $1.95 coils on the page.
http://www.tubesandmore.com/