In my opinion the whole question the LAV being C130 transportable is a red herring
The RNZAF has only 5 C130 so even if they could go the whole distance non-stop, to deliver 20 LAV’s to say Fiji would take aprox 3 times as long as hiring a Roll on roll off ferry and delivering the whole 20 in one go.
NZ to Fiji is 1265 miles. At 45 knots, a vessel like
HMAS Jervis Bay would take 24 hours, which is pretty close to the time it would take to generate 20 sorties over that same distance with 5 aircraft. As far as the Kiwis are concerned, C-130 transportability may not be a big deal. They do, however,
have C-130's. The Australians found it worth their while to fly M-113's to East Timor on C-130's.
The big deal about C-130 transportability for the Americans is that, if it can't go by C-130, the next step up is C-17 or C-5, and those can carry Bradleys, which is a much more potent machine. If you were an airborne task force commander, and you got to choose between having a platoon of Bradleys or a platoon of Strykers, which would you choose?