Did you actually try to book it through the OneWorld site? I had a QF issued ticket last year that most definitely had an invalid segment but booked on the OneWorld site and it ticketed within seconds. Mine was a married segment I forced to break without the 24 hour stopover, but the OW site was very happy to ticket it via QF without talking to a human. If the OneWorld site is validating it, I'm surprised it won't auto-ticket on QF. I talked to a couple human agents before going that route and they refused to try to force it to break, said it had to be XXX-ZZZ and couldn't enter it as XXX-YYY and YYY-ZZZ without the 24 hour stopover.

BTW just reading what you've written above, if they're telling you that you have 18 segments instead of the allowed 16 then you have one more somewhere else that's invalid. BOS-LGA / JFK-LHR is only 3 segments because of the somewhat ridiculous surface segment across Queens. You could just drop that segment entirely and pay cash for BOS-NYC on your own and it'd drop you down a segment, shouldn't be more than $100-150 for that one, but still sounds like you have an extra one in there somewhere else that shouldn't be. Any other surface segments?