In the recent times of the 1880s in NZ we have town/city cemeteries and very few church cemeteries. My gt grandmother would have been classed in NZ as high-ish Anglican.
Her stone does not have the cross in it, only the letters and below that the lilies. I don't think I have seen the cross in it and if I have I have not thought it was a part of the IHS.
NZ Anglicans have an empty cross, ie no actual figure to signify 'he is risen'. RC in NZ have a cross with a sculpture signifying Jesus.
https://www.episcopalchurch.org/glossary/ihs/What is the meaning of IHS in Anglican Church?
a contraction derived from the Greek word ΙΗΣΟΥΣ, Jesus, used as a symbol or monogram: later misunderstood as a Latin abbreviation I.H.S. and expanded variously as Iesus Hominum Salvator, Jesus, Savior of Men; In Hoc Signo (Vinces), in this sign (thou shalt conquer); In Hac (Cruce) Salus, in this (cross) salvation.
http://www.rootschat.com/links/01rqo/Well I have learned something. I think the lack of the cross running through it takes it from rebellious to commonplace in Anglican. It is often carved in gothic type writing within a circle but no cross.