Have you checked land grants in Canada for your Carroll loyalist. Canada has far better records than the Bahamas, a lot of our records are missing or destroyed(hurricanes, fire, neglect etc). I found info on my Thomas Carrol by land grant, slave registry/returns,manumission records, newspaper and CO's. If you find the marriage records for elizabeth it might name the father, then I would check for a will and so on. Are you experienced in doing this, I have been doing research for 1-1/2 years and still learning. Also, Do you have Genealogy.com data library, its in the basic package. If you do your search in the loyalist database they do have many Carrolls, you must check this out.