[Arran]

What does it read from each leg of the high voltage winding to the center tap? The resistances should be close to equal, or voltages if you are applying power to the transformer. From what I know of the way brand Z did things the transformer was likely marginal to begin with, any overload would cause a smoke show even if the set was using a 5Y4 or an 80 instead of a 6X5. As Morz said the high voltage winding should measure in the 100s of Ohms not thousands, so the meter should be set on the 1000 Ohm range, if you don't get a reading then the winding is barbecued. If it's shot get a larger power transformer as a replacement if it will fit. Stupid brand Z sets!
Regards
Arran