Sorry I can't be of much help to you, but I am also looking for information about the Brigg family from Bermuda for the roughly the same period of time you are searching. My husband's gr.-gr.gr.grandmother was Mary Briggs. She was born in Bermuda in 1788 (or 1786) and died in Mansfield, Nottinghamhire on 26.June 1870. On 28.Oct.1810 Mary Briggs married George William Dixon in Doncaster, Yorkshire. They had 11 children, all but 3 emigrated to New Zealand.
I wonder whether Rebecca and Mary Briggs might have been related.