I've been doing a lot of research on FT lately concerning oneworld awards using American Airlines AAdvantage miles. The consensus appears to be that a less-than-24 hour stop is a "transit" and not a "stopover." Therefore, the following itinerary would count as 19,643 miles (assuming each of your stays in LHR is less than 24 hours):

LAX - HKG (stopover) - LHR (transit) - TLV (stopover) - LHR (transit) - LAX