That's a good list and I realise it is foolish to claim I have accounted for all of them. And I now think I am probably wrong saying that George the son of John Carter and Amy Bull is probably the one to marry Ann. But he is another to add to the list (and there is no baptism for him in Paulton.) In the census here he is:
1841, Paulton: John Carter 30 butcher, Amey 30, Thomas 14, Phebe 7, George 4, Samuel 1.
1851, Winterfield, Paulton: John Carter 44 butcher, Amey 44, George 12, Samuel 10, Elizabeth 8, Emma 6, John 4, Hannah 1, all b Paulton.
This George is not with his family in 1861.
But perhaps we can accept that the one who married Ann is the same one who is living with George Hughes in Llangattock in 1861. It would help to know what his relationship with George Hughes is. George must I think be George HEW (bp 24 Dec 1820 Paulton), son of James Hew and Mary Hewish. He married Margaret Lewis on 11 Mar 1852 in Llangattock (stated to be the son of James "Hughes"). I'm not bothered by the Hew/Hughes thing. It would be natural for a Welsh census enumerator and a Welsh vicar to take Hew as the common Welsh Hughes.
Number 4 on your list, George the son of Joseph and Betsy, comes into play now. His mother is Betsy or Elizabeth HEW. There seems to be no baptism for her but her age in the census suggests a birth date about 1817. I can't establish a relationship between her and James / George HEW, but there is a nephew Edward HUGHES aged 10 (b Beaufort, Brecon) with her in 1881 in Paulton.
I haven't managed to dig out anything more substantial - Edward seems to have disappeared after 1881. Betsy Carter nee Hew died in 1887. And George Hughes alias Hew and his wife Margaret seem not to be in the census after 1871 either. But I suppose a possible scenario is that George Hew/Hughes and Betsy wife of Joseph Carter are siblings. Edward is George's son. And these connections make it more likely that George Carter, who is with George Hughes in 1861, is the son of Joseph and Betsy Carter.
Then there's the conundrum of George Carter the lodger with Joseph and Betsy in 1861 - New Town, Paulton: Joseph Carter 48 coal miner, Betsy 44, Henry 14, Mary 9, Sarah 6, Felix 3, George Carter (lodger) 22 coal miner, all b Paulton.
Could he be enumerated twice (not impossible!)? Is George the lodger not Joseph and Betsy's son? I think I saw an earlier thread on this. The son is here, anyway:
1841, Paulton: Joseph Carter 25 coal miner, Betty 20, George 1.
1851, New Town, Paulton: Joseph Carter 38 coal miner, Betsy 34, George 11, Elizabeth 7, Henry 4, all b Paulton.
Hmm.