Just a couple of things. Have you got the details of Barnet Fullard's marriage ? If so, what is his fathers name ?
I now have found Barnet family in the 1891 census. I have a copy of it also showing John. I can let you have a copy if you wish. I found it just by entering childrens first names.
You will never guess how it has been transcribed. The surname has been written down as Fullwood. The typewritten christian name for Barnet has been transcribed as Varney, but looking at the original census, I read it as Barney.
Everything else ties in nicely because of the following, which I am not sure if you have.
Barnets first wife Jane died in 1885 aged 29 years (I have the GRO ref) He then remarried Susannah Hartshorne in 1889 (again I have the GRO ref)
All these records tend towards the view that Barnet was born about 1852 as you say.
BINGO - I think I have now solved your riddle.
I have found him in the 1861 census and also in the 1852 Dudley Registration District births (which covers Sedgley)_ in the name of BARNARD FULLWARD.
I am not sure how long you have been genealoging ??? but I have come across these spelling anomolies in my ancestry too.
The problem was that in those days, many of our dear ancestors
could not read or write, so that when children were registered or they were baptised, the people writing down in the information had to write it as they thought,
Anyway, I would now be 99.99% certain that we have found him (I don't say that lightly, because in my own ancestry, I will not accept anything as correct unless it reaches that sort of level).
Let me know what you think, and also if you want me to send you any of the information I have found.