Well...you haven't looked very far - or very deep - have you.
To save you the time and trouble of researching your own career, let me tell you that there are NO facilities for JAA professional training in the Miami area.
If you go either South or East from where you are, you will drown, if you go West, Naples Air Center is the ONLY JAA approved school on the Gulf Coast (at the time of writing this) and they can only take you to PPL stage (with a multi rating if you wish).....but I doubt that they are three hours drive away from Miami - whatever condition your car may be in.
If you go North - up the I95 - the nearest school (at the time of writing this, though rumoured not to be for much longer) is International Flight Training at Stuart Airport in North Martin County. They say they can take you right through from zero to CPL with ATP knowledge - just DONT pay anything up front, not even a deposit.
Next one North, is at Ft. Pierce, St. Lucie County. European Flight Training. They too can do professional training - but groundschool will be in UK.
Last chance is Orlando Flight Training in Kissimmee. They are approved for professional training - but have no staff to teach it...and I heard today that they have not flown a single aircraft for the last two days due to some insurance hang up.
That's it mate - there is NOTHING else (that I'm aware of) approved in the whole of Florida - for professional training.