All.
Thank you for your replies.
To Flyer1015 - the JFK-MIA will be American Airlines. So we land at T7 and transfer to T8.
Looks like the immigration is the problem so I will book the later AA flilght to give us 4+ hours rather than just 2.
As I say I am BA staff, so the first flight will be in Business Class (and the route to MIA is full in Club hence the look for an alternative route!) on staff travel. The flight from JFK-MIA can be either staff travel or commercial. It all depends on whether the flight looks empty enough!
Thanks again!