SCM: Why not just set the Time Synchronization to update from a New Zealand NTP server.
Snap's DNS server 202.37.101.1 also runs a NTP server on it.
I have not tested this myself yet though so it may not work
NTP server already set to 202.37.101.1... So time is in sync and correct etc, issue is really just somehow telling the Fritz Box when and how to apply daylight savings time.
From Wikipedia:
NTP provides Coordinated Universal Time (UTC) including scheduled leap second adjustments. No information about time zones or daylight saving time is transmitted; this information is outside its scope and must be obtained separately.
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I guess Snap could possibly setup a different NTP server that adjusts for daylight savings, specifically for the Fritz Boxes? Though still kinda broken, seeing as other devices using the Fritz Box as an NTP that know what they're doing would be screwed up.