You mentioned a painless rewire.

In the OEM wiring the ammeter is located between the battery and everything else. This is so the ammeter is only registering what is going in or out of the battery.

When the car is operating and the battery is charged the ammeter will read almost nil. All current in the system used by primary systems and accessories will be supplied by the alternator not the battery. If the alternator fails the battery supplies the current and the ammeter gauge swings to discharge.

If the ammeter isn't the last thing before the battery it can cause violent swings in the gauge when accessories are energized.

If it is correctly wired and the swings are violent it could be a bad gauge or sluggish Voltage Regulator as somebody already pointed out.

Did you switch to an Electronic Voltage Regulator?