The standard alternator is marginal, even with a standard electrical system. A lot of people upgrade to the falcon alternator (mentioned above) when they upgrade the stereo, the headlights, the cooling fans, or when the standard wires seem to be dissipating enough power themselves. So try that.
As for the coil, yeah, the ballast resistor should drop the voltage, but I assume you are either measuring on the high side of the resistor, or you don't have one installed... because it should drop the coil voltage more that 1 volt.
You seem to be loosing about a volt in the wiring, so running a dedicated wire would not be a bad idea. Having said that... 12.3V should be sufficient to energise the coil, so I'm surprised it is that causing the problem.
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