The Horseshoe Route 1940-1942 - Robert Clark
http://www.nzstamps.org.uk/horseshoe/index.html
A super resource in pdf and online formats, hosted at the New Zealand Stamp Images website here recently published in 2019. Includes rate information in the appendix
Also good research resources from the site's main homepage - lots of information on other countries, not just NZ
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I've known this site for several years and it is very usefule for mail anywhere along this route.