Here is my view on the subject regarding the travel to nz to start with:
When traveling abroad for hunting , you want to have a rifle in a common caliber with ammunitions easy to find on the shelf. Because if your separate luggage containing the ammo are stuck somewhere or in transit that rwill uin your hunt . So no fancy wildcats caliber or rare caliber( in nz) like the Nosler ones. The following:7 rem mag,300win mag and 300wsm are common to find in New Zealand gun shops including the Hornady precision hunter line of cartridges. Your hunting distances will be reasonably short ( certainly below 500m) so these three rounds will perform well for the conditions and the animals you will chase in NZ. If you are going to bring your own reloads, make sure to test the feeding of every single round in your rifle prior to departure so as to ensure no nasty surprises when you arrive. Second thing: I think that if you are going on the last trip of your lifetime,it is imperative to have a second scope ( it can be a slightly smaller and cheaper one but with a similar balistic turret graduation or system ) onto a reliable and repeating mounting system pre sighted in. The blaser mount works well as well as the picatinny mount. So if your primary scope fails, you have a second one to replace it and that can be zero checked with just a few rounds. Regarding going to NZ with your rifle, as mention before, you need to be well prepared in advance with your outfitter who will sponsor you for getting your firearm visitor 's permit . Getting in at the Auckland or Christchurch airport with a rifle used to be a straight forward formality, but with the government anti gun agenda of late, a few people got there firearms stuck at the airport police station recently. The situation got sorted out at the end in some cases but with lengthy phone calls to the relevant people at the Wellington police headquarters. There are elections in September that will hopefully will remove the current anti gun government in place and make things easier .
And hopefully also, the borders will reopen for tourists to come in with out too lengthy quarantine periods.
With your budget , you could easily get a second barrel chamberd in a more powerful or exotic round (like the 300 ultra mag) for your elk shooting at long range. If you choose to go that way, you can go with the blaser system ( although I don't think they offer that particular clambering on their catalog) or a custom action with switch barrels . If you go that way, it is easier to have an action with a fix recoil lug . Defiance, lone peak , terminus ...etc would work well. It is preferable that the gunsmith who does your work do fit the two barrels in your action and help you to get a small barrel bench wise ( I think Sinclair makes one) and wrench for when you want to change from one to the other. Good luck your project.