Yes still researching. I am in the process of creating an 'all Gatenby Family tree' on ancestry and read your query with interest. The Jane Ann Gatenby you mention wasn't listed on it so it proved decisive bait for me to follow up. And sure enough I have some answers for you.
I have found her in all the England census from 1861 until 1911 and she remained a spinster.
First her parents. I believe her father was Thomas 1820-1863 and her mother Mary Ann FIRBANK 1827-1908.
Oddly she is not with her parents in 1861 as you mention and the loss of her father when she was only 5 or 6 years old must have had an impact on the family as she did not appear again with her close family until 1901 when she is with her mother. Her mother is described as 'deaf' in 1871. I have only found one sibling of Jane Ann who is James born 1860. He is shown as a bricklayer and is shown with his mother until he married in 1887. His occupation is significant as the John Smith, who is said to be her grandfather, is also a bricklayer. His son William too.
Now the relationship with the Maynard's as shown in 1911. I have found a link. Jane Ann has an Aunt Eliza, the daughter of John Smith. Eliza married a Jacob Wright in Easingwold in 1873 and they had a daughter Effie Eliza born 1879. Effie married your Matthew Maynard in 1905.
I have not been able to confirm how John Smith is the grandfather with the Jane Ann.
Any more info then email me firstname.lastname@example.org