Hi Blair,
Not much further progress, I'm afraid. Its like I've got a jigsaw puzzle with no picture on the box, some of the pieces are missing, and some pieces that may not belong in the box.
The 1861 couple at Burnham seem a good fit (right names (except for the absent s in the surname), right occupation, and one born in Stroud), but if the ages are correct, Joseph would have been 16 when they married. I'll assume they said that they were younger than they actually were. Then there is the granddaughter Mary A COX (Mary Ann) - there is only one birth and corresponding christening that matches the name, age and place, but her mother was Mary COX (no father listed).
Have you noticed that the children's ages in the 1841 Census don't quite match the birth dates from their christenings. I think that the Vicar made a couple of errors made in recording the names and birthdates in the register - Harriet's name has been missed out, and Eliza has been given Harriet's birthdate (the 1841 Census shows that Eliza and Thomas were twins). Maria was christened in 1836, yet the 1841 Census suggests that she was not born until 1838 - could be that the first Maria died, and the next baby girl was named after her. I wonder if the threat of an epidemic, or an illness already apparent in Maria was what prompted the christenings of all of the children.
In answer to your questions:
1. I don't know, it was unusual for the time - maybe a few miscarriages/ infant deaths?
2. They may have been in some of the missing parishes or there might yet be entries, just mistranscribed. The problem is that they didn't stay in one place, so we don't know where to look
3. I think that I've solved (without proof) that one.
At least we do have some confirmation of facts.
A few snippets that I have found that may turn out to be relevant: In Pigot & Co's Directory of Berks, Bucks, Cornwall, Devon, Dorset & Glos 1844, there is an entry in Bristol Gloucestershire under Taverns & Public Houses for the Blue Bowl, run by Henry Walters, Temple back; and also one for a Retailer of Beer, Thomas Walters, at Hotwell Rd Bristol. I can't help wondering if there is a connection there. It might be coincidence, but here was a marriage in High Wycombe Bucks of a Henry Christoph Walter in 1805.
Regards
Sandra