Work permit
I'm a former French army helicopter pilot, with 3200 h and more than 2000 hours on twin like AS532, I also have a FAA ATP H. I have tried to get a work permit, the answer was: NO.
It's hard to get a visa to work in a company, I asked many of them if they need a foreign pilot and want to make him a contract, once again the answer was: NO.
Hopefully my wife is a nurse, got easily a job and I got the working permit 3 months ago.
So don't be afraid to try many ways to find a solution.
Good luck.