"Someone had the idea of tapping into the 440V control grid pin to create a voltage divider with a 470k/12k which works out to around 10V to power the heaters."
Absolutely flaming not, the heaters need in the area of 3 amps of power and the 320 volt winding is capable of supplying (guess) 125-150 ma, thus the heaters need something like twenty times the current available from the HV winding, so eliminate any whisp of that thought from your thinking.
"Without any tubes in I have continuity between the two sets of heater wires."
Ummm, this amp as schem'ed in Doug's library and as pic'ed in your pix has no tube rectifier so there are not "two sets" of heater windings, there is only the single center-tapped 6.3 volt winding. If you mean you have continuity across the 6.3 winding, including to its very own own center tap, from both sides, then OK. Nominally, the DC resistance of a heater winding is very, very small, it can easily be less than 1 ohm. Which is about the resistance of your test leads.
If this amp was working right now, there would be no problem at all with the insulation being cooked or burned off the heater CT and the HV CT (other than esthetic) as both are common and both are grounded. However, whatever created that condition may well have burned stuff up inside the power transformer. Many times, a PT can survive this. A stickler would probably immediately go for replacement and it could be argued that that is the smart thing to do in any case. I wouldn't, in the first parts-buy.
It's not dead certain that you need to replace the power transformer. It's likely, maybe even a greater then 50/50 chance, but not certain.
I think what I myself would do is as follows:
Get your nose as close as you can to the power transformer and smell it. Burned smell? Not good.
-Build a light bulb limiter.
-Take some stranded wire, strip it 1.5", pull a single fine strand of the wire from the bundle, and solder it across the fuseholder. Remove the fuse.
Look at the fuse, if there is one. Blown? Did someone throw a 20 amp fuse in there? In any case, remove it and place a new batch of fuses of correct size on your parts shopping list.
Ideally, I would like to have a 50 watt, 5K resistor, and connect it to the unfiltered output of the HV rectifier, to see if the PT can handle roughly 100 ma of current. I will assume you don't have such a thing.
-buy & install all the parts needed to replace all the parts under the doghouse (all the filter caps) including all the power resistors, the 2 x 220Ks and a 1K and a 4700 and 4 qty 100K resistors, all of these 3-watt metal films like what Doug sells. IOW, on the assumption that you wish to proceed to fix this versus throw it out, completely rebuild the filter section with all new parts. It wouldn't be a bad idea to replace the six diodes in the rectifier with 1N4007 or the 3-amp ones if you want to go NASA. They are cheap enough.
-plug the amp into the LBL
During the following, you are NOT going to turn on the stdby switch, only the power switch! Be sure you know which is which and if you are in the habit of flipping both switches on at the same time, be sure you are not about to do that. Even better....CUT a wire that connects the rectifier to the filter caps, or cut & tape a wire leading to the stdy switch.
Put one tube, hopefully the worst-looking 12 a_7 into the amp. Or...if the pilot lamp is still good, that could do the deed. Position the chassis open-side down.
Power on. Tube lights up? Add another. another, another, another.
Now you know if the heater winding can power up the tubes. leave the amp on for a while. Hours.
[ Ultimately, I think you are going to want to take the PT apart, meaning, cut the wires, remove it from the chassis, unscrew the four bolts, and examine the interior to see if any burning occurred inside. Unless you want to directly proceed to buying & installing a new one. ]
Next, you are going to find out whether the HV section works.