Yes, they do seem to baptise in batches, except... The FreeREG transcriptions of the non-conformist christenings do actually state that William and Humphrey were both born on 24 April 1822 - they were twins unless the transcription is wrong. With no further mention of Humphrey I assume he died as an infant, and I'm still playing with the idea that William was baptised twice, but accept your caution that there are two.
I've turned my attention to Solomon too, testing out all the older suggestions made on this thread, and am quite happy with how things are going if we take Solomon's parents to be Nathan and Ann. Some interesting things come up which may be relevant to both Solomon and Phoebe. Both of them have a gap of about the same decade in which no siblings were born:
Elizabeth Potter b 1808
Solomon b 1809
Harriet b 1810
***
Ann b 1821
Bathsheba b 1824
Phoebe Banham b 1812
***
William b 1822
Humphrey b 1822
William/Sarah Ann/Eliza...
Some hypotheses for the gap:
-Children born in this gap were not baptised at all
-Children born in this gap were baptised non-conformist but the records for that decade are missing/destroyed/never existed/not yet transcribed online
-No children were born - were the fathers absent together, in prison, abroad or posted elsewhere for that decade?
If the non-conformist theory is true, it is worth bearing in mind that Bathsheba was baptised in 1825 in the same Wesleyan church in New Buckenham as William and Humphrey, but Ann had an Anglican baptism in 1821. The Potter and Banham families might have been part of the same Wesleyan church at some point but at least for the Potters the continuity is not straightforward.
