Well done on getting that job!
I unserstand that you have done the FAA ATP theory in 2007. First check if it will be valid when you do the checkride, else you will have to retake it in the US.
With your ICAO ATPL, you should fulfill the FAA requirements, and I understand that the company flies you out to GA (Georgia, US) to give yout the rating training? Then all you need to do is to go a few days earlier, get a fresh FAA medical, do the written if needed and clear beforehand that your Designated Examiner who takes your rating checkride will also do your ATP checkride at the same time. Should be no problem, but make sure they know in advance and agree.
good luck! IP