As I recall, one field wire should get battery voltage from the 12V side of the ballast resistor, which also feeds one wire (the blue one) at the regulator. The other field (green) is wired directly to the voltage regulator.
My guess--and this is just a guess at the moment--is that you're getting a voltage spike in that field wire, something called "flyback", when the relay de-energizes. The larger the coil, the larger the flyback... and you've got an entire field coil's worth of it (a metric shit-ton). In that brief moment of shutdown, that voltage spike across the field could be well over 50V, which would make that last bit of alternator rotations really, uh, effective. Essentially what's happening in that split second is the similar to what's happening in your ignition coil every time it fires. The high-voltage coil excites the lower one, the field voltage goes wild, and it all goes out using your main power wire as a spark-plug wire, so to speak.
Ditch the relay, wire as OE, and I bet your gauge woes stop immediately.