The FAA - JAA conversion is a bit of a b***, but managable (done it myself).
You will obviously need the right to live and work in the European Union, but I assume you have that sorted saying you may soon be living in Ireland.
Be aware that getting into BA and / or Virgin is a hard piece of work and timing. There's hundreds (thousands) of British / European pilots who are desperate to get a shot at them.
Unless you come with a good amount of total (jet) time and preferably on a type they are recruiting for, don't plan on getting an invite soon.
Ryanair and Easy also require you to hold a type rating on the respective aircraft, but if you'd have the experience to go in as a captain should the need be there, you'll have a good shot.
Bottom line, flying isn't the same here than in the States. It all has its up- and downsides of course. For you, it may well be a great thing. I know many Europeans who would love a shot at a flying job in the States. It's all about perspective.