The root servers aren't the problem. They are heavily anycasted and i'm sure there are many in .nz. If that was the issue you could simply serve the root zone yourself, at least some of them allow axfr. [0] This info is also easy cacheable, they have big TTLs and you only have to do it once for each tld. The authoritative name server of the domain you want to access on the other hand are often just in the US or Europe and are the main issue.
Thank you for the correction, I did get that wrong. To be clear, there was no easy solution to get reliable, low latency DNS responses from my own resolver without breaking keepalive by forcibly caching entries longer?
Not that I know of except from having a big cache and many users that keeps it warm. As I said you could run a local root zone but that only saves you the one time lookup every week+ of the tld name servers and the root servers are generally very close to you. There is a map of all root servers. There are 12 in .nz alone. A few cc tlds are providing their zone via axfr [1] so you could add that to your resolver to save some roundtrips but I don't think having .ch or .se locally will make a big difference and they are 1.2GB each and you would need to download them daily.
Edit: How to serve the root zone locally with unbound. https://old.reddit.com/r/pihole/comments/s43o8j/where_does_u...
[0] dig axfr . @k.root-servers.net