If you could read continuity with your meter between the neutral and the ground the breaker would trip immediately and there would be no delay like your describing.
Based on the simple concept of a GCCI monitoring what goes out to what comes back I'd try to rule out a problem in the shared neutral.
I'd take the multi wire branch circuit out of the equation to see if the symptoms changed at all.
Maybe there's some small residual return current that the breaker doesn't like since it's monitoring not only the microwave circuit but another one also that doesn't have a load on it.
For a test, Tie the 2 hots together and bring them to a single pole arc fault breaker in the panel and see if the problems still exists.
I've never been a fan of using a shared neutral for the type of scenario your describing but that's just me.
I've always pulled dedicated circuits with dedicated neutrals to 1p breakers.
JAP>