So... Just to summarize, please correct me of I'm wrong.

Info- I am a EU citizen. Working in the us (dual citizen) and have my ATP, and greater than 500 hours in type, CL65. It's a PIC type.

All I'd have to do is the 14 written exams, to convert? And I can do them through somewhere here in the US (I've heard Florida) or would I need to go to Europe? I'm also slightly confused about why the countries matter so much, aside from fees.

Example scenario, I'd like to apply to a British carrier like BA/Virgin....so any info on how to reach that level of eligibility would be much appreciated. Thanks!