Just an update:
I have discovered Edward Poole the illegitimate son living in Stretton Grandison and referenced in Mrs Ann Poole's will in 1833 as being a 'near relation' to Benjamin Biddulph (not actually named as his half brother), so he lived to grow up and continued a member of the family. I have not discovered any marriage or death for him yet.
James Poole married Ann Bennett and I have this now with plenty of evidence. Ann came from Somerset and was the daughter of William Bennett Esq. They were married in Somerset where James Poole is shown as Captain James Poole of the Parish of Ludlow.
I did want to properly identify Mrs Ann Poole since the Cooper option never seemed quite right, so I'm quite pleased to have resolved this matter.
I still have the huge mystery of the Reverend Edward Poole's wife. She was a wealthy woman and obviously well connected, and it's a real puzzle to me that there is no record to be found - not an announcement, not a marriage settlement or a will - nothing to indicate her surname at all. Perhaps they married out of the country?
I am continuing to work on this, and will update here if I learn more. Hopefully someone with the answers will spot this thread and make a comment!