If you are still trying to keep the original dates and would like to take a risk with two separate tickets you can still do it without overnight:
1) Fly ATW-MIA-ATW. (with at least one extra stop).
For example, on Nov. 5-12 you can do this for $332 on DL.
2) Gayman Airways is flying MIA-GCM on Tuesdays.
For example,MIA-GCM Nov 05 04:20 pm-05 05:50 pm
and return GCM-MIA Nov 12 07:10 am -08:40 am
This will give you plenty of time to make it to MIA and get back to ATW
211.81 USD
Perhaps, you can fly to MIA on Saturday, spend a few days there, and then go to GCM on Tue.
Jet Blue flies FLL-GCM but making connections without overnight would be problematic.
Good luck!