There are tri- quintuple- octi- deci-specialists out there. They're called the Big 4: Earnst & Young, Deloitte Touch, KPMG, & PriceCoopersWaterhouse. They have specialists in every country, and love to take on cases like yours. They'd assign a topnotch team of UK, US, and NZ guys to co-ordinate your advice. If between the two of you, you earn a mid to high six-figure salary, it'll be well worth it to take that route.
If you're not in that income bracket, their price tag will be too expensive. In that case, I'd hire a dual qualified specialist (US/UK, US/NZ, or NZ/UK) and hire a second expat specialist for the third country; or hire three expat specialists. This will cost you far less, but you will need to do the co-ordinating of the advice yourself. It may make sense to have the specialists either meet with you at the same time or else arrange a teleconference call, so that they can feed ideas off each other and get a synergisticly whole solution that's better than any of them could come up with on their own.