Ullevi I got my CAA CPL(H), my FAA CPL(H), IR and CFI at HAI. I now work for Bristow flying the S61 on the SAR contract. PM me if you want to ask questions.
I have to agree with Ablatros a bit, HAI do pick and choose their staff. They also try and sell their services, they are after all a business. Dont hold your breath of getting a job with them though, there are a shed load of people wanting to wrok for them. I hung around HAI for months to see if they would give me a job, didnt happen so I came home. I was the FIRST person to go through HAI and do all the above. AND I got my PPL in the UK, so could be usefull as an instructor for the CAA/JAA course at some point. I thought so at least, my problem was I didnt kiss up to the senior staff, hence I left the US and got a job with Bristow. Which in hindsight suited me far better.
To be fair though, the CAA ground school was GREAT, with G Bedford in charge it ran pretty smooth. And the flying side was good when I flew with CAA (UK) trained instructors like Alan Boswell etc. If you do go to HAI, and want to come back to the UK after your JAA CPL(H) expect to readjust somewhat. But it is worth going, just have a plan in your head as to what you want and go for it.
There is work in the US for hour building, but the likes of Scotia and Bristow dont really care if you have 150 or 1500 hours. What makes a difference is having a JAA IR etc. If you are the right person in the right place and pass the interview you get the job. Its hard to say anything specific as to how to get a job, as its all a gamble.
Good luck and enjoy the ride.