Thank you. I found some information about the Miller Transitron circuit here:
http://www.r-type.org/articles/art-135.htm
Most interesting. Having hooked up the anode and g3 of V3 to another scope, I got the waveforms shown. The first photo is a free running trace, the second is with a 1kHz signal applied and with sync.
As Adrian suggested, the ramp is not linear which would explain the distorted symmetry of the displayed waveform.
I noticed another problem though. When the velocity control is adjusted, I expected the timing to go from slow (fully anticlockwise) to fast (clockwise) with the waveform gradually tightening as the control was rotated clockwise. Instead, it goes from slow to fast to slow with the waveform compressing in the middle of the range and widening close to either outer limit of rotation. While this does correlate to and goes some way to explaining its behaviour (it would sometimes almost sync at either end of its range), this doesn't seem correct behaviour?
When I have a bit of time I will investigate further.