Thank you so much for this. His very limited time there does make it rather difficult.
I stumbled across the census record for the James Moses in 1870 and the age is certainly about right but it was an incredibly common name in Wales at the time (there are around 5 or 6 James Moses' in my family alone that I can think of).
There is a good chance the the post-census James Moses is the one I'm looking for. All I really know for sure is that a) he wasn't around for the 1871 UK census, and neither is his son and b) he had another son, Moses Moses, born in "Hyde Park, America" in 1871 (according to the 1881 UK census upon their return home).
There is also the rumour of an illegitimate child (or children) circling around this generation of the family so the possibility remains that the mother of the young James Moses (1869) was not married to his father (I certainly can't find any British records pertaining to it, and have been going on something I was told by a distant relative who heard the name Rachel Morgan being thrown around) and did not come with him - only joining the family upon his return to Wales.
This also means that Moses Moses of Hyde Park could have an entirely different mother and I get the impression that there would be no birth records for him around that time in that area.
Perhaps this family mystery is meant to remain that way.
Nevertheless, thank you so much for your help on this