Just checked S P for deaths for Jessie between 1911 and 1940 and none of them seem to fit with her details eg. either married or dates don.t match well enough.
There is one in a Rubislaw Hospital died aged 88 in 1918 ,single and no parents listed but she would have been born in 1830. Says occupation weaver, so is obviously a different Jessie than the one in poor house....... Maybe this is Williams mother ??
Another one who I thought previously was Williams mother was from Alvie Inverness. She was unmarried and living with her parents Everything matched until I found William was 11 months old in 1861 census ,and I know our William was born in 1863.
I will on keep searching, like you say it becomes intrigueing
Regards ab