Abel Tasman's descendants on the Coromandel?

Detail from what is believed to be a portrait of Abel Tasman (pictured) and his family, 1637. From Wikipedia.

A bit from the November 2011 newsletter of the Mercury Bay Historical Society (Whitianga) caught my eye. 

"White Street, between Albert Street and Cook Drive, is named for the descendants of Abel Tasman ... It was his descendants who came to live in New Zealand. Abraham Bennet White married Princess Ono of Ngati Awa. They lived in the Whakatane area, but when Abraham was massacred in 1867 members of the family fled to Whitianga to be with his brother, George, who, we believe, was the first European on the "flats", where our town now exists. George built the trading post in Robinson Road."

Abraham Bennet White's murder occurred during the Hau Hau period of the land wars of the mid 19th century, near Opotiki.

REPORTED MURDER OF MR. BENNET WHITE. 

We are indebted to the courtesy of F A Krull, Esq., who arrived from Auckland on Tuesday by the Taranaki, for the following information relative to another revolting atrocity reported to have been committed at Opotiki by the Hau Hau fanatics. When at Tauranga, the s.s. Taranaki was in company with the Government steamer Sturt, and a report was made by Captain Fairchild that Mr Bennett White, who, it will be remembered, gave the most conclusive evidence against the murderers of Mr Fulloon, had been brutally murdered, decapitated, and his head carried about in triumph. It was further said that a native mailman had also been murdered, and that the Arawas were anxious to proceed in search of the rebels, but were not permitted to do so pending orders from the Government. The atrocities must have been committed some days ago, as Captain Fairchild of the Sturt, previous to meeting the Taranaki, had proceeded to Auckland under hopes of meeting his Excellency the Governor, and only returned to Tauranga on finding H.M.S. Charybdis had sailed for Wellington. 

 Wellington Independent 11.7.1867

According to Rootsweb, Abraham Bennet White (1818-1867) married Mere Te Wia. His parents were Abraham White (1782-1818) and Theodora Elizabeth Rudolphina Von Dri(e)berg (1790-1860). The Von Dri(e)berg connection seems to be the one folks say stems from Abel Tasman. There's this comment from a Rootsweb page, from Anne Williams:

"Friedrich Wilhelm von Driberg was Commandant of Mullaitivu at time of his death on July 6,1807. and was probably son by his 1st wife of Diederich Carolus von Driberg who was a Capt. Lt. in the Dutch Company's service at Chilaw in 1766 etc. According to Governor North they were Hanoverians and judging from their arms of baronial rank. Charles Driberg, a descendant signed a marriage register as "Driberg" and later as 'Drieberg''. The von was dropped early. Apparently this family is in no way connected with the family of Driebergs descended from Johannes Gerardus, who married Johanna Horn. The von Dribergs married into White with the marriage of Theodora  .Eliz. von Driberg to Dr Abraham White. Note honorific VON not VAN the latter being the Dutch equivalent both denoting someone of importance.The above family was never VAN. It is supposed that this family was related to Abel Tasman. It would be interesting to learn how."

I'd be interested as well. Anyone out there with some ideas of info, please do get in touch.