That would be a dipped shellac, which is pretty much going to ignore acetone. Dissolves in methanol quite nicely, and as you are going to be making a new pressboard former for it in any case I would suggest a very simple method, which is place it in a small tin box and make a fire with it inside for about 5 hours. Then open the tin after it is cool, and dunk the charred mess in methanol overnight, then wire brush the char off till you can undo the bolts, then take it apart.
The paper insulation has gotten moisture in it, and then carbonised to create the ground short. Use high temperature wire on the new one, and at least 5 layers of kapton tape between the first winding and the paper former, then a single layer of the kapton tape per layer. First turn use a PTFE sleeve for extra insulation, as it likely arced there first. Bonus is that it will be a lot less bulky with the kapton tape, and the number of windings is not as critical, provided you fill most of the core. Just note where the air gaps are and put back the same way. You can varnish it after winding, but with modern tape and wire it will not be needed.
The common field fix for these shorted chokes was simply to undo the 4 bolts and place the whole choke on 4 20mm long plastic spacers so that the live case would not touch ground. Works, but the choke case is then part of the B+ circuit and is at high voltage.