Gonvil - are you aware that part of those checks done by the FAA require a response from the UK CAA.......and that the UK CAA are refusing to do it??
There is, currently, a major stumbling block with regard to the "conversion" of CAA to FAA licences.
It would do you well to start studies towards gaining a full FAA PPL - by means of both written test and skill test (known to them as "check ride").
The written can be done in UK before you come here - and is information that you will need to know anyway.