RJC. This is my two pence worth for you...
At 36 I was going through a mid life crisis, like you, I really wanted to fly for a living. Spent 17 yrs working in London, and wanted a change.
I sold my house, car, motobike, parachute, dog, everything. Moved to the US and worked in PA. I obtained all my qualifications up to CFI. I was very lucky to be able to secure my work visa, then green card to follow. I taught for over 2 yrs, then moved to company in the GOM. Now fly tours in Alaska for the summer, not quite sure what to do after though
Wouldn't mind working back in the UK to be nearer my family.
I have heard rumours that a larger GOM company may be sponsering visa's due to the lack of pilots around. If that would be the case, you my consider moving to the US, perhaps on a J1 before they take it away, then apply to this company once you are a CFI with 1000hrs. Or at least speak to them about the visa's before you come.
Just my quick thought on the subject
Good luck with whatever you choose