Hi Mal,
I don't want to give you information you already have. Not that there is much, is there? I have searched for Jane and James with no real result like you.
You already had the baptisms on your tree so you know about the discrepancy with mother's maiden name.
Mary's baptism shows an address in Juno Street in 1881 but the family are not there in the census that year.
The other baptisms don't have an address but Sarah Halligan is the Godmother on both those. I wonder if we could find her?
Do you have any birth certificates for the children to compare Jane's name, James' occupation and any addresses which could help?
Regards and Happy New Year
Heywood