About 5 years ago when I was in Las Vegas, I met a Briton who was being sponsored as assistant manager in the hostel (he was more so Regent, waiting for the Princess to become a Queen). He had been there 2-3 years, and they wanted him to stay longer but he wasn't interested. So I'm sure it's possible.
Which visa category you fall into, I don't know. Correct me if I'm wrong, but I believe J is a business investor, and H is highly skilled employee. You most likely fall into the skilled employee category like it has been suggested. I've also read that the 66,000 is not currently being used up (maybe it's another category I'm thinking of). Either way, you're best seeking professional immigration help on obtaining an US visa - it's worth spending $200 (maybe less) to get a bunch of options that will affect the rest of your life.