All booked, paid and ticketed now. ^ ^ ^

Took Darren's advice (thanks) and booked CUN-MIA-BOS then will do surface down to NYC. Other than that, two slight changes (no LAX-LAS, and going home via NAS instead of BGI).

Interesting news
(maybe you all knew this already but I was pleasantly surprised):

We had no problem at all booking, paying and ticketing with the delightful people at the BA Travel Shop in Manchester, even though it was ex-BLQ (Italy) with a Euro-zone fare. Also, they charged Mrs AntonH's Amex (she needs the points) in Sterling, having converting from Euros at the mid-point rate. So we avoided the credit card exchange spread - i.e. this would have cost us about 2 - 3% more if we had paid locally in Italy with Euros.

I don't know if this would work for other fares (e.g. ex-IST/CAI/WAW), but may be worth a try one day for anyone based in the UK who wants the fare but not the ticketing-/payment-related stress of a non-UK origin.