You really should take a close look at the sticky thread up at the top of the forum heading.
DFW-JFK-SYD-CNS-SYD-HKG-BKK-HKG-LHR-AMS-LHR-YVR-DFW
Would work but you would be wasting a lot of possible segments, 4 in North America (but only 2 stopovers allowed because it is your continent of origin), 2 in SWP, 2 in Asia, and 2 in Europe.
For mileage try the
great circle mapper.
Prices can be found
here.