Long-time lurker, first-time poster . . .
This is the classic presentation of crossover distortion. There'll be a fault somewhere in the vertical amplifier, between the vertical position control and the deflection plates. In this condition, the input signal has to overcome the "turn-on" voltage of an amplifier stage before any output voltage is generated - see your middle photo with the small positive and negative "bumps".
Check all the transistor base-emitter voltages. There'll be a transistor or two which is biased "off" under no-signal conditions, or even a complete failure.