The Lee Enfield NZ carbine used a barrel with similar exterior dimensions and taper, but it is not made from a Martini barrel blank as some believe. The nocks shape is different and the stub is a wee bit longer on the Lee.
A Lee Enfield barrel can be shaved to fit a Martini, but a Martini barrel will fall a coontaire short of fitting a Lee. Headspace is miles out.
The front sight block on the NZ carbine is the same as the Martini Enfield unit, yes. Small machined block, barleycorn with protector ears.
The Trade pattern 'carbine fitted to accept P1888 bayonet' used a regular Long Lee rifle sight block.