Your analysis of this mystery (who are parents of Frances Elizabeth Hoag) parallels what I have learned (1850 Census of Simeon W. Gunn and his wife- Sarah, and an adopted child- Frances E. Hoag). I am confident this is Frances. I feel this way in that Simon had acquired some wealth as a farmer of Kirkland town, Oneida County, New York, and in that county were several prominent schools for girls.
Frances achieved what girls of that period only dreamed of...a high school education immediately followed by under-graduate studies in a foreign country; to wit, Toronto, Ontario province, Canada. It would be there in Toronto while attending a university (name of university most likely was "Old King's College", Toronto City) that she met her husband- Reuben Berrey (born: 1835, England).
I have completed some research during 1999 - 2001 regarding HOAG surnames in Dutchess County, New York. One reference I refer to regards the period during our American Revolutionary War, in which Dutchess County offered her fathers and sons to defend the territory of New York and to assist General Washington's Army.In 1898, James A. Roberts had published in a 2nd edition book "New York in the Revolutionary As Colony and State"[i] those militia units which were formed out of New York. The following information was drawn from those militia units that held militiamen with a HOAG surname:
1. p. 382:Five HOAG family members listed in these pages: 237, 242, 246 & 249.
A.p. 237:In the Albany County Militia (Land Bounty Rights)- 16th Regiment, listed two enlisted men:
B.p. 242:In the Dutchess County Militia (Land Bounty Rights)- 3rd Regiment, listed only one enlisted man:
C.p. 246:In the Dutchess County Militia (Land Bounty Rights)- 5th Regiment, there was listed:Major Brinton Pain (Commanding Officer) with his staff comprising Adjutant Isaac Crane, Captains Joshua Barnum, Israel Vail, and Veal, along with, Lieutenant Samuel Curtis.Additionally, only one enlisted man as:
D. p. 249:In the Dutchess County Militia (Land Bounty Rights)- 6th Regiment, there were identified 24 captains and one enlisted man being:
A second reference I refer to is the 1880 U.S. Census of District No. 41, Middle Kiowa, Elbert County, Colorado, in which the Enumerator was Honorable Reuben Berrey- husband of Frances. Details were documented between 1 - 30 June 1880. In this census, a very high confidence level can be had regarding the data collected by Reuben since he personally documented with accuracy that the parents of his wife were both born in "Connecticut". In 1880, Frances was 43 yrs old.
A third reference I refer to is death certificate of Mrs. Frances Elizabeth (Hoag) Berrey. According to the death certificate of Frances E. Berrey (registered with the Los Angeles County, Bureau of Vital Statistics, California State Board of Health, Local Registered #238), her oldest son Charles Reuben Berrey provided family information which provides the first clues to her parents- realizing today that "Walter" may in fact (as you stated) be "William".
Charles listed her father as "Mr. Walter Hoag", born in England (not true; born in Connecticut), and her mother’s maiden name as "Ms. Carrington" with no place of birth given (born in Connecticut).Additionally, Charles gave the date of birth for Frances as "31 August 1837", and that she was born in New York (true information; however, no town or county was provided by Charles). With this information I was able to compare with details obtained from the U.S. census between 1850 – 1900, resulting in the place of birth of Mr. & Mrs. Hoag (parents of Frances E. Berrey) being "Connecticut".