Many, many thanks for that. It makes life so much easier if we can transit in FRA rather than re-checkin because of our separate booking reference.
I have just called ICC and the FRA-DUB was available and booked.
That route was
NO, NO, YES, NO, YES, NO and YES, all in 24 hours.
I will say that all the ICC staff were very professional and offered advice, but occasionally not thinking of the cost in miles (like "book the LAX-ORD and FRA-DUB" so you don't lose them"!) That would have cost so many miles.

Job done and time for a drink!!