Romagic,
Honestly, I'm still going with the voltage drop caused by running your microwave too.
They typically draw up to 10+ amps when you turn them on. The Autopilot itself, can also draw up to 10 Amps during normal operation. That's a pretty hefty load if they both 'peak' at the same time.
On my boat the B&G autopilot(network pilot) has a 'Rudder Reference Unit (RRU), which is a sealed high specification potentiometer, it determines it's pointing by measuring voltages in the sensor at the 0.10 volt level. You can measure the voltage difference between the green and blue wires of the RRU, which should show a minimum of 1 volt change from hard over to hard over. It is also here at this same connection that You could connect a Voltmeter and determine 'IF' there is a current fluctuation (spike) when you Turn Your Microwave ON/OFF. Keep in mind it will only take a 0.1 volt change to throw it off, when you turn the Microwave ON. You can perform this task while tied up safely at the dock.
Now my Network Pilot 'glitches' now and then, but especially when the house battery starts getting low, which makes it more sensitive when a major electrical appliances is being used, such as the normal on/off cycling of the refrigerator.
Good Luck with yours!
James