So I did some more research and I think starting in RUH makes a lot of sense. With BA's "taxes" and surcharges it ends up being more than ex-AMM, (~$11,200 VS. ~$10,600) but the positioning costs to Saudi Arabia are cheaper AND I'll get to experience more F without using any RJ flights. New proposed routing:

Positioning: SEA-xDFW-xLHR-RUH and return

1. Riyadh (RUH) - London (LHR)
2. London (LHR) - Bangkok (BKK)
3. Bangkok (BKK) - Delhi (DEL)
4. Delhi (DEL) - Tokyo (NRT)
5. Tokyo (NRT) - Beijing (PEK)
6. Beijing (PEK) - Hong Kong (HKG)
7. Hong Kong (HKG) - New York (JFK)
8. New York (JFK) - Vancouver (YVR)
9. Vancouver (YVR) - xDFW - xSFO - xORD - Seattle (SEA)
10. Seattle (SEA) - xLHR - Nairobi (NBO)
11. Nairobi (NBO) - xLHR - Riyadh (RUH)

The American routings are just for mileage and any other suggestions, even of an added destination somewhere else in the world would be appreciated.

Also, I know that getting a visa for Saudi Arabia can be very difficult, but am I not correct in thinking I'm fine visa-free in RUH for less than 24 hours?