A few things :
- You can book AA.com tickets from outside the US, but you need to ticket them from the local ATO. I do this in Cayman all the time
- Re BA online ticketing, you should be able to call the BA 1800 number and get them to honour everything you see on the website, even on instant purchase fares....I have done this and they do recognise the problems for ticketing travel originating outside the country of credit card address.
- Re LHR-EDI flights, there is lots of frequency and BA and BM both have pretty much equal schedules, so no need to pick one over the other based on schedule.
- If connecting from the US to LHR-EDI, make sure to pick a flexible ticket over the cheapest possible, as since BA/BM introduced the latest very low fares on the domestic routes (to compete with the LCCs), they no longer allow standing by on earlier flights, so you could end up with a frustrating wait in the lounge if your transatlantic flight gets in early (as they often do)