The Aussie pilots are right. A friend in NetJets America said that they have over 90 aircraft on the way for 2023 and require at least 700 experienced pilots. They are finding it difficult to find as the airlines are hoovering up available pilots. The sim centres are struggling to keep their instructors as the airlines are taking the ones that can still pass a medical.
We're recruiting too, but not at those numbers.
The biggest hurdle for people wanting to shift countries is the right to work/visa. Then the licence conversion.
If I were you, I'd stay in the US, finish off your training with the best scores etc possible and then be prepared to move where ever the work is. Have a mental list of who you'd want to work for and why, check out their bases and requirements and try and match it.
Good luck