Mary's letter to Ralph, presumably in Australia.
So Mary Allport (daughter of Sarah Hawkins Heaton's brother, cousin of Annie Heaton) wrote to Ralph -- making it before 1894.
Robert Jamison had escaped bankruptcy by having Mary Allport bail him out at Annie's request.
(So the debt-paying was before his death, not after as I had assumed.)
And ... he was living with Annie, who had three daughters at the time.
She refers to Annie's three pretty children: Florence and Dorothy in the 1891, and Eveline born shortly after.
I can't understand the letter fragment that appears before that one, though, from Mary Allport to someone. "Ralph was a bright funny fellow" (despite his bad heart and inability/unwillingness to work, per her letter on his death). So it has to be post 1894. She sends her kind regards to "your husband. I am offering to take care of a few things, when he was going to be sold up". So it is before Jamison's death, whenever his near-bankruptcy was, and before the letter to Ralph talking about bailing Jamison out. Which doesn't make sense.
Eveline's letter says that the birth certificate she finally got as an adult shows her born 10 October 1891, to the former Annie Hawkins and John Richard Heaton. She says that per her birth certificate, he was a journalist. Well, that makes him a perfect match for John R Taylor in Annie Heaton's household in 1891. I suspect that question is settled!
Annie's marriage certificate shows her as Annie Heaton, widow, with father Ralph Hawkins.
Eveline was Annie's third daughter. The birth certificate for the first daughter, Florence, in Deptford in 1888, shows Annie Heaton as the mother and no father.
After those daughters were born, Annie seems to have invented a consistent backstory for herself, as a woman married to and the widow of a Mr Heaton, who was formerly a Miss Hawkins. Her mother's surname was presumably the convenient one to use for the story. Since she was in fact called Annie Heaton all her life until her marriage to Mr Powell, she had to invent the other bits. Including John Richard Heaton.