Just a further thought ...
I see from your Ancestry Family Tree that James and Letitia had four children - William Henry (1842), Anne (1843), James (1845) and Francis ("Frank") (1849).
I presume that Francis was born in NZ, but both William Henry and Anne appear on the GRO indexes (curiously, no sign of James, though). Additionally, William Henry's birth was registered in the Wycombe RD which covers both Oxfordshire and Buckinghamshire. As Stokenchurch is right on the county boundary with Buckinghamshire, I wonder if that's where Letitia comes from - and did she "go home to mum" for the birth of her first child? (Anne's birth was registered in Thame, which includes Stoke Talmage and South Weston.)
Have you purchased a birth certificate for either of these two individuals, as this may confirm the maiden name of Letitia?