Well, Frontier would be good to train with, sure. You also have the advantage of half dozen schools in NZ that use Cabri.
The syllabus 'forces' you to work on sling and mountain, can fly the solo time (ie learning the advanced sling stuff) or nav to meet EASA requirements, or bit more, if going for the FI rating later. For that, now it's 250hrs total heli and 100 euro PIC (not FAA post-PPL dual) but if doing 30hr course, need 220TT to start it as minimum if you got the command hours..
I would NOT however make any solid plans as foreigner in NZ job market, even if you somehow sorted work visa or residence (doable in other skills/jobs). NZ exports newbie Kiwis to Australia, tuna boats etc, as it's bugger all pay for newbie FI job and few between. Sure, can try loading chemicals few years for chance to fly R44 or 66 or 500 on ag ops. Not advisable for someone from abroad wanting to fly soon as.
The other day one guy posted on Oz specific heli forum (and Nz), same guy who was FI rated CPL from Nz, done Aus TTMRA rubberstamping conversion to Oz and it's year since asking first time for ideas, already a grad. NZ has too many heli pilots of all experience levels, many of whom work abroad due jobs. While it'd be great experience, seasons, mountains, utility oriented companies that do training, etc, I'd just go the US route if I were you and funded. Dollar's too strong against Euro now, sadly, giving us all grief who save AUD, EUR, GBP etc to burn in USA on flying..
I'd avoid Mauna Loa if you go for F1 visa, too costly, less likely to work for them, handful of bad feedback (along the lines conditional job offer and need to fly more solo NVG etc to meet the NVG training endo only to be ignored after).
Quite a few German speakers and other Europeans ended up marrying/settling in US. It's not all fat ugly chicks some anti-whatnot would like you to believe. Though the mentality is different as well as family values, but that's life and not everyone..
There are other legal ways to stay on in USA, not just F1 for ab-initio. Just have to ask/research.. As well as Nz, which doesn't have as strict migration criteria as Oz. Yeah, and cheaper. Except for paying lawyers in US, Australia has the highest migration/
PR fees to govt and associated costs, of all English speaking countries and I've had some exposure/dealing personally.