I made a solenoid for the new motor from 1290 turns of 34 swg wire - the earlier version used 40 swg wire. The plastic part and the nail were the same as previously. The coil resistance of the new solenoid was 19 ohms. The solenoid can lift 30g a distance of 6mm when powered from a 12 V source. It doesn't require the additional electromagnet that the previous version used.

The motor will operate with a torque of 2.5 N cm on the shaft, that is about 3 times larger than the largest torque that the previous version would work with. The escapement mechanism will release when there is a larger torque than that, but then slips rather than stopping on the next tooth. This could perhaps be remedied by altering the tooth shape.

The photo below shows the old and new motors side by side.

This video shows the motor operating. It is being switched by a homemade relay, which is in turn switched by a relay clock made from two SPDT relays and two electrolytic capacitors.

I came across this very interesting paper about the factors that influence solenoid performance:

A Detailed Explanation of Solenoid Force by Paul H Schimpf