No, it is not doable, and you are breaking the most important rule -- you cannot leave your country of origin a 2nd time. So when you arrive back in LHR, you can fly up to 4 more segments within the UK (to MAN or EDI, for example), but you cannot leave the UK. Purchasing extra segments within the continent of origin is also not allowed. In practice this means if you originate from another country in Europe (not UK) you must use 1 or 2 segments to get to/from LHR, so you cannot do both Greece and Israel legs from LHR. Might be better to originate in Japan; in any case, I guess you need to rethink your routing, or plan on buying some extra tickets to fill in the missing legs that aren't allowed on the OWE.

Alternatively buy your ticket after April 2007, when RJ joins OW and you can fly JFK-AMM (though that may not be the best way to get to Israel). However you state leaving in December, in which case you are limited to the current 8 OW airlines and cannot book flights on RJ, MA or JL.