Thanks for all the info so far. To address a few questions posted:

While I am interested in accruing as many miles as possible, I'm not really interested in adding a fifth continent to this trip. My stops in the states are to visit family/friends and aren't really flexible. DFW was the logical choice because I can buy a cheap R/T ticket to Tucson, and it only burns up one segment each (HNL-DFW, DFW-EWR). While JFK might be a better option than EWR, it is much easier for my Dad to pick me up/drop me off at EWR than driving into Queens.

I've decided to replace Manila with Singapore. It looks like a nice ride via BKK only using one segment on the inbound flight, and outbound 2 segments via JAL.

Coming back into FRA, then staying overnight and departing for Amman the next day (via LHR- BA, RJ). Then, I would turn around and catch the early TK flight back to Germany via IST (no OW miles, but a few half-hearted miles towards SEN ).

The AMM-HKG direct flight is not showing up via the OW booking tool. I know it continues on to HKG, but for some reason it isn't coming up.