The invocation of the Oneworld help desk (which seems to act as the strict parent when the Oneworld ticketing desk children squabble) has solved matters.
There is the slight problem that I can only get my ticket reissued at an airport AA desk because the RTW desk cannot take UK credit cards.

I have just made a trip to BWI airport only to find the desk closes at 18:00 - it would have been nice if the AA desk had mentioned this.
I suppose an AA UK call centre could do this too, now I think about it.
@Bukhara
You were partly right about the flown vs in-flight sector issue. This is why nothing could be done while I was waiting in JFK for my JFK-BOS flight: the HKG-JFK sector was still in "check-in mode" (AA RTW desk's words).
But I think the underlying problem was what you call DCS control. It would explain why it only became apparent after some investigation, since I am not trying to check-in. The DCS controls have been lifted and the ticket can be reissued. Why they were imposed remains a mystery.
Are you able to explain - for my benefit and potentially future RTW'ers - what these are? I have never come across them before and I fly a lot (although not as much as some people around here

).
@RTW4
Am I right to think that Cathay should never have refused to change the US sectors in the first place, since the ticket is issued on their stock?
The AA RTW desk tonight were quite shirty about the fact that it is a Cathay ticket and they were having to do all the hard work - especially when one of the changes might be to take the CX YVR-JFK flight instead of an AA SEA-JFK flight!
I have to say, I am not impressed by some of Cathay's processes. They seem to handle xONEx poorly, their call centres do not inspire confidence that the staff are in English and I seem unable to select a seat before check-in despite being OW Emerald so I keep getting crappy seats.