I can't go over to to EU and start flying planes around for money the same as you can't do it here. What on earth gives you the right to deny me or one of my pilot colleagues (Aussie born or
PR's) a seat in a 737? We have no pilot shortage here and never will. Some companies may find it hard to attract quality applicants but that is only because they probably aren't good employers to start with.
If you were unemployed with a family to feed I may have some sympathy but by your own admission your single and fancy free with a permanent contract.
If you want a change of scenery you could try the vast number of agencies recruiting for the Middle and Far East airlines.