Well, after many hours of puzzling, shifting with flights and looking at various options, I came up with the following. I have added 'just a couple' of flights to my original itinerary...
I downloaded the RTW Mileage Calculator from the Star Alliance website. It works quite good although I think I found a few glitches. For example, it claims that I have more than 24 segments in my itinerary, which is not true.
Here we go!
BKK - NRT: probably Singapore Airlines (777), although I'd like to try ANA (767).
NRT - SEA: United Airlines 777. Looked at ANA NRT-SFO and UA SFO-SEA, but no miles left!
Overland from Seattle to Phoenix via San Francisco, Los Angeles, Mojave and Las Vegas. We plan to do a scenic flight over the Grand Canyon, probably with a Scenic Airlines Twin Otter.
PHX - DFW: America West (will their aircraft be repainted in US Airways colours?)
DFW - ORD - STL: United Airlines, via Chicago O'Hare to St Louis.
STL - CLT - TPA: US Airways, via Charlotte to Tampa. The STL-CLT leg is operated by a Mesa Airlines CRJ900, while the CLT-TPA leg will probably be my first ever 757 ride.
We'll have a few days in Florida to drive around. We'll also visit MIA and FLL.
MCO - CLT - SXM: US Airways, via Charlotte to St Maarten. Spotters' heaven!
SXM - IAD: US Airways to Washington Dulles.
DCA - YYZ: Air Canada from Ronald Reagan to Toronto.
YYZ - BOS: Air Canada back to the USA.
BOS - LGA: US Airways shuttle to the Big Apple, leaves almost every hour.
A few days in New York, and then
JFK - FRA - AMS: Singapore Airlines to FRA and connection to Amsterdam Schiphol. Apart from spotting at Schiphol, I am going to show some sights to my partner, who is British and never visited Holland.
AMS - OPO: TAP Portugal to Porto, and the next day
OPO - LIS: on to the capital Lisbon.
LIS - MAD: TAP to the Spanish capital. Also planning to visit the beautiful town of Salamanca.
MAD - ZRH: Swiss to Zurich for some business and spotting. We might take the train to Geneva.
ZRH - IST: Swiss to Istanbul, for a week or so in Turkey. We'll probably head down to Bodrum.
IST - DXB: Singapore Airlines to the UAE, and after a few days
DXB - BKK: with Thai Airways back home.
As we can have 15 stopovers during the trip, including 5 in the USA, in some places we'll stay less than 24 hours for them to count as transits.
Phew! Well, the above list amounts to 22 flights (out of a total of 24 allowed) and some 28,920 miles (which is under the 29,000 mile limit of the cheapest business RTW package). I am sure the airport taxes will be considerable, but what the heck, this is going to be a fantastic trip! Lots of new routes, airlines, airports and other things to see and to do.
Never before have I been so eager to spend a large amount of money...