In last year's Budget an additional $130 million top-up was announced for the scheme, but officials note the funding is on track to be exhausted by June this year.
Economic Development Minister Phil Twyford told the Herald budgeting for the scheme was challenging.
"It's unusual - it's an on-demand and uncapped programme, but you've also got to ensure future obligations can be paid. In recent years that's been managed through the annual Budget process."
While unwilling to talk numbers, Twyford did not contest the Herald's estimation the scheme would soon be costing taxpayers $250m annually. Twyford said the spending was worthwhile, as it underpinned economic and employment activity in the screen production sector: "I think it stacks up for New Zealand."
Large chunks of the documents, and all correspondence between MBIE and Amazon officials, were redacted over concerns their release could prejudice ongoing negotiations over the studio's application for a bonus 5 per cent subsidy - worth tens of millions of dollars - if the project was deemed to offer "significant economic benefits" to New Zealand.
Twyford said these negotiations were "moving along quite nicely" and expected them to conclude by the end of April.
He said Amazon would have to "meet all the criteria set out on the rules" to secure the bonus, and he did not believe the production was at risk of moving offshore were it not secured.
Amazon declined an opportunity to be interviewed about the project or the apparent lack of New Zealanders in key creative roles - a criteria for being granted the uplift. The Herald> understands last month's casting announcement, which lacked big-name stars and featured no New Zealand actors, covered all main acting roles. However, auditions are understood to be ongoing for supporting and recurring roles and it is expected several New Zealand names will eventually be included.
Documents and briefings obtained by the Herald also show "Middle-earth" tourism branding efforts of the past two decades, tied to Sir Peter Jackson's Lord of the Rings and The Hobbit trilogies, are likely to continue.
Officials said the prospect of hosting the series would "facilitate the retention and refresh of our 'Middle-earth' brand," while seeing production end up in Scotland would risk its "dilution".
The prospect of Tourism New Zealand and Air New Zealand again pushing swords and pointy ears to promote the country induces cringes for subsidy critic and Act party MP David Seymour.
"When I go overseas and people in North America seriously ask me if I have fur on my toes, I don't feel like it's the type of image New Zealand needs. Being the country of Sheppard and Rutherford and Hillary - that's something I'm proud of - but the land of hobbits? I'm less sure about that," he said.