I've completed my tests of the main transformer and am now 99% certain that it is the cause of all the problems I've been experiencing with this old analogue scope. It's clear there's something very wrong with the large, multi-tapped output winding. Here's the schematic again:
I removed ALL connections from the transformer. ALL the other output windings are giving exactly the outputs I would expect from a given input; it's just the long winding on the lower right hand side that's giving nonsense outputs. As you can see, the centre tap is grounded and there are 3 tapping points either side of it. When injected with a 20kHz sine wave of 50V p-p to the primary winding, the peak-to-peak outputs from the problem secondary at each tap are as follows (from top to bottom)13V 13V 3V 0V (gnd) 3V 1.8V 1.8V
I would have expected these voltages to be symmetrical either side of the0V centre tap, but as you can see, this isn't the case at all. I can only conclude from this, to use a technical term, that this tranny is f***ed. If there's something obvious I've overlooked (which I doubt) please feel free to point it out. Otherwise I'll be opening it up to perform an autopsy over the weekend. Thanks again to everyone who tried to help.