Reiteration of the fact that, especially when unloaded, the speed will go up and up and up until the motor eats it's own brushes and/or bearings.
Classic diac/triac circuit seems to be controlling the field coils direct from mains and the armature from mains AND via the diac/triac.
DC diac/triac circuit adds a 240/9V 50VA transformer and rectifier to provide the field coils with high current/low voltage DC. The mains supply to the armature AND field coils is also rectified.
It's not necessary to wire the armature and field coils in series but this gives the benefit of lower starting current and higher ultimate torque.
But at slow speeds the triac can receive phantom triggers which will cause "glitches".
There is a possibility that this can be fixed by using a two-triac circuit. But this is so far untested.