Need some help with minimizing taxes on a change to the itinerary I want to make. AA rate desk is not being very transparent.

My original DONE3 itinerary was: NRT-DFW-YVR-DFW-MBJ-DFW-JFK-LAX-DOH-MAD-LHR-HKG-NRT (italicized means no stopover)

The one I changed it to is: NRT-DFW-YVR-DFW-MBJ-DFW-JFK-LAX-DOH-MAD-DME-LHR-HEL-SIN-HKG-SIN-HND.

Rate desk came back with additional $334 in taxes/fees. I already figured out that I because I have no stopover in HEL, the APD luxury tax applies for the entire LHR-HEL-SIN distance, rather than just LHR-HEL. Of course, the RTW desk agent was clueless about this and kept claiming that the APD is a flat tax, regardless of the distance. Okay, I can make a stopover for a day in Helsinki, which should drop the APD by $180, so the remaining taxes are $154.

The other thing that the rate desk noted is "Russian taxes". Matrix ITA tells me that the taxes on DME-LHR segment are just $19. Am I missing something?

Also, the DFW-MBJ-DFW was originally $178 in taxes and after change to DFW-SEA-DFW should be just $46 saving me $132 to count against other taxes.

Anything else that stands out?