I can't wait to
see Vectis's face when they find out that the puzzle has been solved!

I will be interested to know if Vectis intends to purchase any certificates. In particular I would be curious about:
The Harrill Simpson Vic marriage (were there any children from this union?

)
The 1893 Harris Moore marriage at West Ham
Also, the birth certificates of Mother and Nellie to see what father's names are given.
Vectis, IF your grandparents DID marry and that the 1893 marriage is theirs, it is strange that you were told they were not married. I would also be curious to know if Nellie
was a half sister. I suppose if the parents were married your grandfather would be named as the father even if he was not. Maybe in this case the family rumours may have the advantage over official certificates (as people may have known the truth) .
Perhaps some DNA tests with Australian Lee descendants may give you some answers.