In principle the circuit should work fine.
I use it for synchronising 2 pendulums at the moment which i will expand to 4 when time allowes.
Each driver has its own driver transistor and coil taken from the same supply, with a 2200 µF capacitor near the 547 to minimise any dips in the supply rail.
I like also to try instead of the steel nut on the pendulum rod, the rectangular bar which is used by the FAVAG clock. I think that way you will get better torque if the timeconstant of the penulum is out too much.
Bear in mind that the Bürk clocks have graham escapements and ± 98 % of the energy comes from the movement, and may be 2 % is used for correction, in case of excessive temperature drift or barometric pressure changes. ( just a guess )
The rod is from Invar, which is an alloy between nickel and steel which hardly expands or contracts with temperature changes.
If you require all the energy to come from the coil then you need to try to experiment with the amount of turns, or supply voltage.
Look at it as the child on a swing principle. You give a push each swing cycle, swing keeps going, you also can give it a harder push each second cycle, swing keeps going.
You push the swing to early extra torque is required, correction in progress.
you push the swing to late, hardly any effort is required and things are running fine. ( It gives the approx. idea how it works )
Any impulsing circuit should work, as long there is a driver which can supply an impulse to a coil.
I have access to precision quartz movements from old power board time switches which have less drift than 2 seconds a month, so these were choosen.
If you have access to radio signal impulses like Frankfurt 1500, I can't see any problem in decoding a 1 second impulse from that to synchronise a clock from that too.