You have misinterpreted the rules somewhat... they do not count stopovers (except in the continent of origin, where the limit is two) - what is limited is the number of flights segments (i.e. single flight number on a single ticket coupon, even if the plane stops somewhere). You can have 6 segments in North America (including the Caribbean) and 4 segments in each other continent. In addition you are allowed the intercontinental segments, which means three in total in a 3 continent ticket.

Note that a stopover is defined as 24 hours or more, so you could, for example, spend almost a day in Hong Kong in transit without it counting.

Go here for a complete copy of the rules for OneWorld Explorer tickets:

http://members.shaw.ca/fewmiles/oneworld/

In your proposed itinerary you have too many segments in Asia (7 rather than 4) and potentially too many stopovers. Also 15 segments in N America (only 6 allowed). The Europe part is OK.

Roughly, "Europe" includes the Middle East. From Pakistan eastwards is Asia.