As you say so much "fits". As AB says, Jessie can be the diminutive of Janet or Jean.
Jessie's maiden name on the Lancashire Witch is "Struthers" in the alphabetical index at the front of the manifest but "Strathers" elsewhere - and reported as "Strathes" in the newspaper list.
In '61 "Janet Caruthers, age 21, Domestic Servant, born Maybole" is working in Lanarkshire and in '63 a "Jessie Struthers/Strathers/Strathes, Lanarkshire, age 23, Dom Servant" arrives NZ.
Can you find a Janet Carruthers, born Maybole 1839, parents Moses/Elizabeth in OTHER THAN NZ after the '61 Census - eliminate her as "your" Jessie.
Re last post I think I spotted John on a FamilySearch passenger list of '62 - will revisit.