But it is striking that NZ is ethnically very Scottish, yet has no trace of Scots in the accent.

There is a trace of Scots in the only distinctive regional accent within NZ. Southland has its own accent, distinguished by being markedly rhotic, in sharp contrast with the very non-rhotic NZ standard.
FWIW, your mention of Kent interested me, as my sister, born and bred in NZ, was often asked by prisoners of Mother England if she was from Kent.