Mate, if you want to do IAH-EDI, the best way to do this was Delta IAH to ATL then take the DL 97 direct from ATL to EDI. Did it EDI-IAH in cattle class a whole lot of times since Delta put the route on last year and never had a bad flight. Myself & a few colleagues did this trip quite a number of times for work and talking about it, we all agree that it's better to have the transatlantic leg as the last leg & all the better if it's overnight as well.
Unfortunately, Delta pulled the EDI-ATL flight back in October and might eventually replace it with an EDI-EWR service in mid May next year, we are still holding out collective breath
As a result, you are probably better to fly from houston to Newark (EWR) then on to Edinburgh on Continental. By all accounts, you don't get as good a standard of service on CO across the pond as you do on DL, but CO are better within the US. So all in all, you should be OK.
I personally wouldn't be booking through AMEX, as they have proved uneconomic & unresponsive for our purposes and we now book our own travel individually. If this is for corporate reasons and your firm happens to have bases in dunfermline, Fife, Scotland; Kongsberg,Backerud,Norway and Singapore, then we do it all individually now now in the Engineering department and the others are currently following suit.
Hope this helps.