Indeed, photos of your Gent C-7 Master Clock would help.
You ask in part: "it seems there's not enough current flowing through the circuit. Indeed, when measuring the current using an ammeter, it seems only a couple of dozen milliamps are 'going through'."
Without a diagram of your "circuit." I don't know exactly what circuit or part of the circuit is being observed.
I would suggest that you measure the current at the most basic part or element of the time transmitter, the reset electromagnets. When the circuit closes, the current should be 220 milliamperes. The simplest scheme involves removing one of the connections to the reset electromagnets and inserting your ammeter in the circuit. Then, manually close the circuit to observe the measurement. Close the circuit with a wire jumper, or in some way short circuit the contacts.
The Gent and like time-slave systems operate in a current loop. The master and all slaves are "daisy-chained" in series with the entire "loop" being supplied with an intermittent 220 Milliamper current each time the master circuit closes.
If there are no slaves in the circuit, no current will flow. If only the pilot dial is present in the loop with the master time transmitter, then enough voltage is needed to provide between a minimum of 170 mA.
Nearly every Gent C-7 has at one time been used with a system of secondary or slave dials and including its pilot dial. In a phone central office, 48 volts is readily available and is generally used for the clock system. A variable adjustable resistor or "rheostat" is generally supplied and mounted in the master case so as to adjust the current to through the loop. As a rule of thumb, each additional secondary or slave dial requires an additional 2 volts approximately. Thus a C-7 with no slave dials and only it's pilot dial in the series loop, should operate with three or four volts supplied to obtain the required 220 milliamperes.
Analysis of the Gent or Synchronome system is best done by reducing the circuit to it's most elementary configuration; that is with only the master and a couple of dry cells in series; no slaves and no pilot dial.