Taking a break was the magic sauce, admittedly I have removed all but one of the US domestic legs so the overall mileage is reduced but that 'allows' me to work on the HKG-BKK-DOH or HKG-XXX-XXX-DOH portion of my plan - magically OSL-MAD has flights again.

Hopefully I can add the US domestic legs back in once I get the far east portion sorted out, although I may try approaching a travel agent with a valid 15 segment trip and ask them for any suggestions to add a convenient 16th segment.