OK, I've desoldered the EHT board from the scope and then powered the thing up again. The regulators to make 5V, 12V and 24V on the main PCB all produce voltages within spec. Unfortunately I only have the schematic for the scope (not the manual), so I don't know what voltages should be on some of the other test points around the various boards.
On the EHT board, there are 4 big (0.1uF) polystyrene caps that look like they're not original. They sit over the resistors that have obviously overheated, and whilst a couple of them appear to be a little marked on the outside by the heat from the resistors, they appear to be working (I'm testing them with the Ohms range on my multimeter, and the resistance measurement increases for a few seconds and then indicates open circuit).
I've desoldered one end of C601 (which appears to be a Ceramic disc cap), and it seems to be open circuit (no charging up). Should I expect this, or might this be a culprit?
Additionally, the board shows a little sign of scorching around R604, which is in parallel with this capacitor. R604 still measures the correct resistance.
The Tant cap on the schematic (C606) looks for all the world like an electrolytic, but has a little yellowing on the side. I can't tell whether this is because it's been smoked on by the stuff, or it's overheated.
If you lift the 2 burned resistors, does the oscillator run OK? Do you get high voltage out of the transformer?
I've not tried that (but I will). The burned resistors measure to have about the right resistance though (which is why I thought they may be a symptom rather than a cause).
Going to check the various diodes and then see if I can find a bench supply to run the board outside of the scope.