I got my postdoc in NZ (and then Australia) by doing a collaboration during my PhD with the guy I ended up working for. Wrote a couple of fellowship applications and got one of them. My current postdoc in the US I got by applying to 30 odd jobs on various websites and this was one of the the 2 or 3 video interviews I got.
I can't speak for the US, but I know Australia and NZ have a points system for people wishing to immigrate without a sponsoring employer (if you can get a job offer while in the UK, you're golden, as they say), where you get a number of points for each degree you have, years job experience, net worth etc etc. You should be able to find out the details online somewhere.
For geosciences, your best bet would be one of the big oil/gas/mining co.s in Western Australia as they were hiring like crazy last time I was there and the wages were crazy. You'll be perched all alone on the end of a continent with a minimum 4h flight to anywhere else, but Perth is supposed to be a lovely place to live. Other than that Alberta or Ontario, Canada, as SK said above. NZ, I don't know. If you're 50yrs+ and have a hankering for "how it used to be in the olden days" or are seriously into outdoor sports and shooting anything that moves, you'd love it. If not, you'd be better off in Australia. I love the outdoors (used to go for 2h bike rides in the mountains on my lunch break

) but I found it a little bit backward and extremely isolated.
As for the promotion feedback, sounds like they're just stringing you along, like they think you're good enough to do what you're doing but don't really care about you. I think a fresh start would be a good idea
