My Baxter Missing Link

Like everyone else I too have my "problem" ancestors. This year I'm going to see if I can't resolve at least two of these brick walls. In this specific case it is Hannah Baxter, my 4th great grandmother. For the past 10+ years I've been trying to verify who her parents are. So what do I know so far?

• She was born about 1801 (range 1801-1803 from census records) in the province of New Brunswick
• She married Charles Howe, son of Lt. Caleb Howe UEL of the Queens Rangers and Esther Fairweather, on 20 Dec 1822 in Norton, Kings County, New Brunswick
• She appears in the Canadian census enumerations of 1851, 1861, 1871 and 1881 in Kings County, New Brunswick
• She is not found in 1891 census so it is assumed she died between 1881 and 1891
• She had had a large family: Robert, Caleb, Ann, Mary, William Small, George B., Esther, Charlotte Willard, and Joseph
• Her husband, Charles, died 7 Nov 1839 in Kings County, New Brunswick

According to the page "Simon Baxter of Hebron Connecticut" at http://freepages.genealogy.rootsweb.ancestry.com/~jcahill/simon.htm Hannah is listed as the daughter of Elijah Baxter and Mary Smith. However, I've not been able to find any document that can substantiate that statement.

So where have I looked (other than the obvious places)?

• Marriage records: "New Brunswick, Marriage Registers, 1789-1889" at https://familysearch.org/search/collection/2001063
• Land records: "New Brunswick, County Deed Registry Books, 1780-1930" at https://familysearch.org/search/collection/1392378
• Provincial Archives of New Brunswick web site including but not limited to "Daniel F Johnson's New Brunswick Newspaper Vital Statistics" and "Vital Statistics from Government Records (RS141)"
• Posts on Facebook groups and Ancestry  message boards
• Google searches for references to her or her probable parents

I've not been able to find a death registration or obituary. I've also not come across a will or probate for her probable parents. I still need to look in the 1887 - 1891 editions of the Kings County Record to see if I can find any reference to her death just in case she died in that period.

So I put it out to all those other researchers, where should I look next? What other resources have I missed in my quest to find out who Hannah's parents are?