The Thomas Gooch you have described is my Great, Great Grandfather, and My Great Grandfather was Thomas Walter Gooch.
I have copies of Thomas and Thomas Walter's police service records and also William Henry's before he died of Typhoid at Adavale in 1896.
Thomas Walter and his sister Charlotte were both born in Ireland, Thomas in County Westmeath in 1847, and Charlotte in Donegal in 1850; the 1851 census has Ireland as the birthplace
for them both.
I think Eliza's mother Charlotte's family name was Littleboy. I have Parish record for a Titley - Littleboy marriage dated 12 Nov 1810, but am looking for further verification.
I am interested in any photographs you may have of Thomas and Eliza's family as I have only a couple of Thomas Walter which I would be happy to e-mail to you if you wish.