WRT segments after stopover: my understanding from a conversation with the AA RTW desk is that intercontinental trips without stopovers count as an intercontinental trip, not as segments.

Example: BKK-HKG-LAX-PSP without any stopovers would not use any segment credits in Asia or NA.

I'm about 25% sure on this but this would explain how HKG_Flyer1 got his free segments after the stopovers.

Perhaps there is not steadfast answer, just the luck of the draw on who makes your reservation...