ORD-SAN-BOS-SJU-DFW-YUL is 9663 vs 7509 for ORD-SAN-DFW-SJU-MIA-YUL and seems to be possible and valid.

And clearly if mileage maximisation is your goal then don't do SGN-HAN overland - do it via NRT, pay US$150 for the 5th segment in Asia, and drop to 4 segments in NA to keep within the 16 limit.

And can't you get full miles on CX flights if they have (and you book) an AA codeshare?

Something like:
LGW-BUD-TLV-BUD-HEL-PVG-NRT-HAN-NRT-SGN-HKG-JFK-SJU-SAN-DFW-YUL-LHR

Is 37432 vs 31565 flight miles on your original.