Hi just a quick thought that might make your life easier.What actually is the difference between a "high torque" quartz clock movement and a standard one, when talking about the modern, square plastic beasts available from Asian factories? Don't they both use the same single AA battery? Does the high torque movement send more current through the coil, drain the battery sooner? If so, does it do so by using longer pulses, or pulses with higher peak voltages, or both?
I was repairing an old Smith electronic clock . So I had a cheapo Chinese movement on my desk so thinking of you I tried some tests that may interest you.
Use the cheapo movement remove the coil from the cheapo movement and use it as the base driver ie connect the out put to the base of a transistor.
And use that to fire up your coil .