It isn't obvious to me why getting the right to work in the US isn't an issue for you, unless you are planning on marrying your partner, but if you say so....
If that's your plan, be aware that a spouse visa needs to be applied for from outside of the country and will take at least six months.
You will need to complete an ATP-CTP course at an approved school like ATP Flight School, which you could bang out in a week. It's 30 hours of ground school and 10 hours of sim and costs about $4,500. Then you can take the written and practical tests. Before you start the course, however, you will need the FAA to validate your foreign CPL, and you will need to apply for TSA approval to undergo flight training in the US. These are paperwork bits that take a little time. The flight schools will be able to help you with all of that and answer any questions you might have. As far as the airlines go, you might get a job at a major airline with just 1500 hours, but your problem is that they probably won't start looking at your application until you get your license and your green card, and you won't get your green card until you move there. You will be likely to get a job with a regional airline a lot faster than with a major, so you may want to apply everywhere and take the first offer that comes along, unless you are happy commuting back to your old job in the UK for awhile.