Not sure which Barnabus Eldridge is the husband of Patience Eldridge.
* Capt. Barnabus Eldridge, son of John Jr Eldridge, Jr & Elizabeth 'Betty' Eldridge
* Captain Barnabas Eldredge, son of Capt. Barnabas Eldredge & Mary Eldredge
If I had to make a guess based on family, I would say Capt. Barnabus Eldridge, son of John Jr Eldridge, Jr & Elizabeth 'Betty' Eldridge, since we have Captain Barnabas Eldredge married to Temperance Eldredge during the same time period.
Anna Hallett is in conflict based on which is her father.
http://services.dar.org/Public/DAR_Research/search_adb/?action=full... has Barnabus (1738-1797) married to Patience Crowell
[https://books.google.com/books?id=OBbq13eCddYC&lpg=PA1095&o... Cape Cod Library of Local History and Genealogy: A Facsimile ..., Volume 1] edited by Leonard H. Smith, page 1095. has their marriage in 1762.
Same book, page 755:
https://books.google.com/books?id=OBbq13eCddYC&lpg=PA1095&o...
John Eldridge, Jr. Married Betty Gorham, July 20, 1737. Their children born in Yarmouth:
1. Barnabas Eldridge, born May 9, 1738.
(which matches the DAR record birthdate)