I'm going to point out a few more points from http://www.rebelpuritan.com/Gardner.html
George Moriarty points out that a George Gardiner remained in St. James Clerkenwell after 1630, had several children, and was still there on Oct. 29, 1657 when "Rebecca, daughter of George Gardiner," was buried. On this date, our George Gardner had been a resident of Rhode Island for nearly 20 years. However, St. James Clerkenwell birth and baptismal records have several children born to George Gardiner, including the Rebecca who was buried in 1657. ...
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From the same Moriarity article:
Asa Bird Gardiner claimed that he found the couple and three sons on a passenger list for the Fellowship, which he said sailed from Bristol, England to Boston, MA in 1637. This claim concludes that Sara and their two eldest children (Edward and Robert) died in the crossing, but their infant son Benoni survived. That would make Benoni Herodias (Long) Hicks’ step-son, not her natural son. ....
The births of Benoni, Edward, and Robert to George and Sara (Slaughter) Gardiner are not found in London vital records. The sailing of the Fellowship with the Gardiner family aboard is not found in the shipping lists.
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What I would expect to prove the relationship between the Rev Michael family and the George of RI family is correspondence, not necessarily vital records. Will is best of course; but letters, financial transactions, ship register, artifacts & heirlooms, affiliations in other family relationships, geographic similiarity, class & education, people in common.
All of that is lacking in the Rev Michael to George of RI relationship.
Conversely, we have a proven relationship between Herodias' third husband Porter & Benoni. There is only one reason I can think of why he would include Benoni with his brothers in the property gift he made them, and that would be: she was his mother.