Frankly, I cannot see what the problem is exactly?
Depending on which country you would like to be your license issuer you are to complete ATPL GS and CPL training in the same country, of which you hold a valid Class 1 medical certificate. Training for your ratings can be undertaken in any other JAA member state. So if you would like the UK CAA to be your license issuer, you must sit your ATPL's there, complete your CPL training either in the UK or at a JAA school in Florida, and hold a valid UK Class 1 medical certificate. The training for your ratings may be undertaken in Germany.
The German CAA do not recognize ATPL GS completed with a UK training provider, the UK CAA, however, do recognize the ATPL GS completed with a German school. I cannot say if the latter really is true so stand to be corrected on that one.
As my previous poster said, do contact the relevant agency beforehand and to protect yourself against all odds get an answer in writing!