Hi Barbara - Reckon it's hara kiri....
The only clues I'm still stuck on is 1ac 'Heath in Tas, to which Cook's vessel takes boy to New York'(8). If this is PANDANUS, then that means 4dn 'We hear the bell tolls for her' (4) begins with the U from (Pandanus) space L space. I thought it would be NELL but that means 1ac would be.... PANDANNY or something, which I can't find anywhere.....