Hi Tracy
Will be in touch shortly via PM.
Yes, as I also suggested previously, it's worth getting the 1930 marriage record (printout) for John Ivan SMITH and Dorothy.

Just have a look though, at the list of children for Annette Elizabeth and William John Bennett SMITH. (There are seven ... last-born (1908) has no father's name recorded ? I am guessing that WJB and AE parted some time after 1903 birth of Helen Daisy ... and WJB has then started his second family ?)
http://bdmhistoricalrecords.identityservices.govt.nz/My "money' is on "Isaac John SMITH - birth registered 1902"
being "John Ivan".

("Isaac" may well be an error on the online BMD? Might pay to check the microfiche record of the Birth Index (at library) if you have access. 1902 registration ... but you say he was born late December
about 1900 ... maybe it was 1901 ? ... often births late in year, are registered in the following year.)
"Lillian" ... hmmm "Lily" .... sometimes this is a pet name for "Elizabeth" (but it may just be that "Lillian" on the death certifcate is an error / wrong info given by death informant?)
The maiden name SIGNAL is a strong factor though ... so yes, I'm going with the "Issac John".
Lu