Welcome to the forum RNeil, my knowledge on the 1917 – 1923 period of the NZ Ordnance has much improved since my last post just over 5 years ago.
You mention the 1NZEF NZ Ordnance badge was only worn up to 1921, and then readopted again in 1923? Is it not possible that it remained in use from 1917 up to 1923?
You also mention the same badge remained in use until 1937 when they followed the British lead and replaced it with the round garter style badge?
The following page from the Unofficial history of the NZ Ordnance Corps in the Pacific 1940 to 1944 seems to suggest it had a much longer period of use.
The following photo is borrowed from page 58 of the book “NZ Army Distinguishing patches 1911 – 1991.”
The photo shows the same badge being worn with the Pacific khaki drill “un-camouflaged” walking out dress uniform.
