You are welcome. I didn't do all that much. My wife's 2nd great uncle was a Scot who fell at Ypres in 1917 while serving with the Argyll and Sutherland Highlanders. I found the Commonwealth Grave Comission when loking for him. Their web site - and the records that make it possible - are amazing.
Genealogy is history at a personal level. Any historian has to sift through facts and make judgements. In our country, that usually means discounting the legend that Great-Great-Aunt Mary Lou was a Cherokee Princess. I suspect that over in Australia, your neighbor to the west, that means accepting the fact that 4th Great Uncle George wasn't really a guard or a sailor on HM convict ship, he was a passenger. I have no idea what the common legends are in New Zealand, but I suspect there are a couple. Royal blood, maybe; it is always popular, whether it is Cherokee, French, Italian, German or English.
After you get the facts straight you have to ask yourself what they mean and what was it like. I just took a guess. Most of the pictures I've seen of NZ in National Geographic show it to be a peaceful green country. Matthew was 19 when he died; his parents were probably still living. I just put a little flesh on the bare bones of fact.
Matthew died violently, 10,000 miles away from home, while engaged in a noble cause. I'd appreciate it if you'd tell the rest of your relatives that at least one American knows that we are in his debt.