Thanks for getting in touch. The one thing I have learned about Llangyfelach and the Rees' is that there are very many of them! It also gets complicated in my family because some of my relatives used the alternative spelling Rhys as their surname. Not aware of any of my clan emigrating to NZ.
The two christian names which figure predominantly in my family are Morgan and Thomas - which alternate for several generations. There are a couple of Esthers in the family but neither fit the dates or maiden names of your tree.
Happy to let you view my tree if you would like - I need your email address to do this.