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I think those are classed as the Herbert flock or type.

As said you can't hunt Arapawa Island atm
Chathams cost 1k round trip on air chats
Easy to orgainise a hunt there and happy to give people names
Once there can stay at pub or hotel or private...

Arapawa Island sheep dont have splotches either, occasional with nose or tail tip.
Pitts are all black finer sheep
Chathams are heavier than both and white

Hunting then on the island is a no go at the moment
You shouldn't be able to get permission from DoC or any of the land holders