Stopovers only count in the continent of origin. You can stop in lhr and hkg as many times as you want subject to the other segment rules. Also, there is the new limit of 20 segments for the entire journey. So you could only add 3 more segments if you add another continent. In Asia, I would opt for a RT to Bali instead of NRT. Need to know which cities are the stopovers in N. America, but if you have to go to those cities, not much you can do to improve the routing. I would also buy a separate LHR-AMS-LHR and use your segments elsewhere, maybe in S.America if you go there. If you travel after 1-Jul, you can earn AA miles on BA flights that depart from Canada, Mexico, and the Caribbean. Therefore, you could go DEN-DFW-MEX-LHR or DEN-DFW-YVR-LHR/HEL(on the AY codeshare) and give up the JFK-BOS segment.