I have just done some chart work on my computer.
From the point at Omaha allow 39 miles to the Needles travelling round the south of Little Barrier.
That is a good trip as you can use Little Barrier to shelter from the wind, especially returning home.
It is 38 miles to Tryphena from Omaha, almost 90T.
The Barrier is such as good place you just keep on going and going. And you can do a lot of miles in a day. I have seen many boats your size at Arid Island and round the back of the Island.
So stock up on fuel or be prepared to buy some at either Port Fitzroy or Whangapara.
I will warn you that you will not like Great Barrier fuel prices, they are expensive, very expensive. They prefer cash but can take a credit card - a little walk to the lodge at Whangapara.
I came across the Colville channel from Tryphena on sunday morning, and we managed it at 10 knots in an easterly swell average 2 metres, big waves at 4 metres with 25 knot SE wind. I have a 9 metre diesel launch. Once into the Firth travelling to Gannet Roack it chopped up real bad so down to 8 knots. I prefer the open ocean as the waves are further apart and easier to travel in.