Its possible that the Palmer's may have arrived in New Zealand on another ship but the extract below from The fartherest Promised Land by Rollo Arnold. Pages 80 - 81 is my best source to date !
“While in Invercargill Holloway met some old acquaintances from Oxfordshire. James Palmer, who he had recruited from Bletchington for Brogdens, told of wages averaging ten shillings a day, since he had arrived in New Zealand on the Zealandia on 4 January 1873. From Palmer, Holloway had some good news of William Terry, a union man from Kirlington, who had also come out on the Zealandia for Brogdens.”
Both James Palmer and his wife Dinah appreared in the 1871 Census records for Bletchington so I know that their departure for NZ was after this date.
An extract with reference to the 'Zealandia' from the Otago Daily Times 3 Jan 1873 states: - “392 passengers, most landed at Bluff. 84 for Dunedin. " I deduct from this that the Bogden Recruits did not appear on the passenger list of 58 as listed for the 28 Dec 1872 arrival at Bluff & 10 Jan 1873 at Port Chalmers.