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His resignation came after the building's owner, Isobel Nikoloff, of Perth, Western Australia, told the Otago Daily Times the project had "stalled".
There have been few obvious signs of work being done on the historic Otago Peninsula landmark since Christmas.
Mrs Nikoloff said this week there were issues with money and with the management of the project: "It will require a strong amount of cash and someone with a strong will to push it through."
Mrs Nikoloff, a retired schoolteacher, said she did not have the cash and being able to complete the building now was "going to be dodgy". It had been an "extremely expensive" project so far.
She initially hoped the building would be completed by last October and that it would now be generating rental income.
She said she was not happy with progress but her attention during the past 16 months had been on another family "difficulty".
"People take precedence over bricks and mortar," she said.
A conservation plan and a programme of work had been drawn up but "there hasn't been a systematic following of that plan", she said.
Mr Milne showed the ODT through the building yesterday and an hour later rang to say he would be informing Mrs Nikoloff he would be resigning.
Mr Milne detailed the work that had been done to waterproof the building - including replacement of the roof and removal of rotten timber.
The wet conditions during the past five days had put that work to the test.
Mr Milne had found no leaks and was pleased to have achieved what he had set out to do. "The building is saved," he concluded.
He considered the remaining building work was "very straightforward" but said he was frustrated at delays because of the difficulty in getting clear decisions from Mrs Nikoloff.
Mr Milne said he had been working on the building for two years and had never met Mrs Nikoloff.
Most dealings were by email and it had taken months to settle on the shade of white paint for the frontage.
Mrs Nikoloff told the ODT she was not happy with the paint's tint.
Before his resignation, Mr Milne said the current project had been to complete the turret and re-erect the flag pole.
There was still money "in the kitty" and an approach was being made to the Dunedin Heritage Fund, administered by the Dunedin City Council.
The fund offers grants but assistance for a private dwelling was "most likely" to be a short-term, low-interest loan.
He resigned "with regret" but considered it was "the only way forward" for the project.
Mrs Nikoloff has owned the building for about 30 years and in 2006 announced she intended restoring the former stately home, designed by Dunedin architects Mason and Wales and built for William Larnach in 1880.
There were initial problems evicting a "caretaker" so that work could proceed and, in 2007, a 127-year-old Italian marble fireplace went missing and door panels were damaged.
The pieces of the fireplace, some damaged, were recovered by police.
Mrs Nikoloff said she had not lost enthusiasm for the project and the house was not for sale.
She hoped eventually it could be used by university academics.