So with a resistor across the contrast control, I don't loose sync when the contrast is adjusted all the way down.
But I still have the same problem with the contrast turned all the way up and a strong signal into the set (connected directly to the modulator as opposed to using the rabbit ears). Putting a resistor in series with the control to limit the high range sort of works, but the sync is still pretty weak with the contrast as high as I like it. That capacitor I added in earlier seems to be a better solution. With that capacitor I get good sync throughout the range of the control (as long as I have the resistor in parallel with it so the total resistance of the control doesn't go too high).
So with both the extra resistor in parallel with the contrast control, and extra capacitor from the grid of the 1st sync tube to ground, and about 80 clip leads
- I get sync throughout the range of the contrast control, and a good picture. See pics below.