Sounds like a sound plan - UK flying is very much different to flying in and around Florida. I find flying around London far more difficult and challenging than flying in Florida, so it's wise to understand local procedures first.
I did things slightly differently; I completed as many groundschool exams in the UK at my local FTO as possible so I could concentrate on flying in the USA. It definitely helps. Some of the guys who were out there at the same time couldn't sit their practice skills test because they hadn't completed the written exams and therefore never got around to taking their skills test.
Lastly, don't forget to factor in the cost of the VISA, flights and living expenses.
You mention OBA...I believe they still do their PPL completion package as geordiejet says.