Too late for an NZ flying safari business -
http://www.flyinn.co.nz/ This operation is in the next valley south from Omarama and they have a great reputation for conducted power plane vacations around NZ. They always have a booth at Oshkosh.
And from what I understand, a fast track for the FAA and the NZ CAA “paperwork” is an oxymoron.
A turbo-normalized Bonanza is the pinnacle of piston flying, imho. But it might be “too much plane” for NZ skies, since your distances are relatively short and terrain is mostly well below 10,000’ msl.
The trouble with a BT tour of NZ is that there are so few Beech products in NZ, and not many more if the fleet is widened to include other brands. Then much smaller if we consider just the planes that might be rented out to expert BTer pilots. And yes, then there is the huge paper mountain you alluded to.
The problem with getting above weather is that you eventually have to get back down. A turbo plane opens a wide array of new flight plan opportunities, but it also brings complex new challenges and decisions as well. In NZ, the weather is very complex micro climates, fast changing, and usually damp enough to make IMC and even ice a concern, even in summer.
And yes, it is a big stretch from NZ to anywhere – akin to flying from the U.S. Mainland to Hawaii, or even to Europe via Greenland and Iceland. A step too far for most of us.