[Arran]

I think you could start by Ohming out the various windings on the transformer, the H.V secondary is usually the one that fails first, the resistance on either side of the H.V center tap should be fairly close, like 35 to 40 ohms, give or take 5 Ohms per side, the rectifier heater winding should be something like 1.2 Ohms, the 6.3 volt winding 1.5 Ohms. Crumbling insulation may or may not be an issue, other then you would have to replace the transformer leads, or sleave them. If the transformer is bad they usually have a strong odor of burned varnish, and tar, along with the paper being charred. 
  I tried to look at the Edcor site but it does not seem to work with Brave Browser, some don't if they have cookies, or block ad blockers. Antique Electronic Supply also has some replacement transformers for tube type guitar amps, both vertical and horizontal mount, the one in the Philco looks like a vertical mount which makes it easier to fit a replacement, none are cheap but all would be cheaper then getting the factory one rewound if it really is shot. 
Regards
Arran