Very good to point out that crossing to Bimini you should start Miami/Ft Lauderdale but I still don't think seven days is enough time to go further unless you are in a power boat
that can go a good deal faster than hull speed
. Believe me I have tried to squeeze a Bahamas trip into a week more than once and the math just doesn't work if you try to go beyond Bimini or Freeport
If you make AM landfall in Bimini it will take you half a day to clear customs
and imigration. Even if you spend no time at all in Bimini you could not get onto the banks before mid day, most likely late afternoon. It is about 70 nm just to reach Chub Cay and another 5-10 nm minimum past that to reach anywhere you want to go. So even if you sail all night across the banks you won'[t reach the Berrys until the next evening, probably after dark (not recommended without good local knowledge). So for practical purposes you would not make the Berrys until the next am.
Now you have used 2 days out of your seven and need to figure the same to get back. So, four days round trip travel time to get 3 days in the Berrys. Can be done but just too hectic for a fun vacation
. Also allows no time at all for any weather or other delays.
Now with a Defever trawler
(what kind of power do you have and what's the cruising speed?) maybe you could do this a lot faster, but for us slow pokes in sailboats doesn't seem practical.