Hmmm. The date of immigration to the USA is given as 1903 on at least one census record, and also on the 1918 passport application, which says he lived 'uninterruptedly' in the USA for 15 years. He did return to New Zealand in 1923 and again later. There is a further passport application in 1920, which mentions a trip to Europe for a month in 1912 and the Red Cross trip in 1918. No mention of his wife anywhere.
That electoral roll with Mildred sounds like the one I saw. The occupation and name sound good, but the wife's name and evidence of a child suggest it's not the right one.
There's the possibility that Kate was a nickname. If my name was Mildred, I'd probably change it too! I know of lots of people from around that time who weren't known by their official names.
From news cuttings in Trove, I got the impression he studied in Bathurst, then worked in WA, then in Melbourne, but he may have lived somewhere else after that.
Of course he could have married twice, if Mildred died, but she was having a child in 1907, so that doesn't sound likely.