Rob
I travel a lot in my job, and I would definitely put AI well ahead of, er, Baghdad Regional Air. I've been on worse (the time where a number of passengers demanded to be let off a Mandala Air flight after they'd had two attempts at taking off comes to mind), but I would definitely go out of my way to choose another carrier over AI.
Have you looked at maybe Air France or Lufthansa to go with a change in Paris/Frankfurt ? This can often be cheaper transatlantic, but of course there's an extra few hours for the transfer.
Regards
Mark