[Arran]

Those resistance measurements aren't too far off the factory spec, though the one reading 272.4 seems a little low if the actual is supposed to be 320. A shorted high voltage winding will have one side substantially lower then the one on the other side of the center tap. A shorted H.V winding will also cause the transformer to heat up even without a load. What you need to check is the voltages on each side of the H.V winding as Terry suggested, they should be pretty close to equal, maybe withing 5 to 10 volts. These sets do cook transformers from time to time but less often then their brand Z counterparts from the same era.
Regards
Arran