^Thanks for all the feedback and ideas, wonderful!

The update is the following:
- I have registered for DEQM
- I have changed my itinerary significantly, to increase miles, use all my segments and fly on airlines that give maximum mileage (eg avoid BA, CX, RJ).
- I will buy from London which will help save significantly.
- I considered changing the order and going westbound, but that won't work. Thanks Njfan07 for the great idea!

Revised Itinerary:
LGW-BUD-TLV-BUD-HEL-HKG-HAN--SGN-NRT-PVG-ORD-SAN-DFW-SJU-MIA-YUL-LHR

Questions:
(1) Is there more mileage possible between ORD and YUL? I'm going to San Diego & Puerto Rico as I have never been but would not mind other cities if it means more miles. I want to earn as much DEQM for all these flights.

(2) When I try to book SAN-SJU via DFW on the Oneworld Itinerary planner, this flight option doesn't come up. However the Oneworld Interactive map & Timetable offers that option. What I am doing wrong? Would it be easier to call AA and book at the LONE3 flights via AA Reservations?

THANKS!