1/ I got one of these and it holds my board, two wings, and all my foil gear (3 wings, 2 stabs, 1 mast) plus wetsuits etc and comes in at 27kg. With a carry on bag its a one-bag travel solution and you can wheel it and get around ok yourself. Admittedly its a small board. Travelling with longer boards requires some planning not so much for the plane but the travel to/from airports, which is a stuffaround.
www.aquatichero.com/2020-cabrinha-av8-foil-travel-bag2/ NZ is a wingfoil paradise, I'd take waternomads up on their offer and hit some waves around Taranaki.
3/ Alternatively - use your trips as an opportunity to annually upgrade your wings and/or foils from a local store, and ask them to loan you a board for a week. If you're dropping a few grand on gear they'll happily help you out with a loaner. Then you're travelling with a mostly empty bag one way, don't have to worry about getting skunked cos your luggage is lost, and then come home with a smaller bag with the wings and foils.
I've done this pretty regularly on work trips to Oahu to upgrade kiting gear. I've even gone over with no gear, used the gear for a week, then the store has shipped it back home.
Its also a nice way to touch base with a local store who can help you out with advice, spares, repairs and any issues you may have far from home