I'm also researching the Mogfords and Mugfords of Bampton, Devon.Over the last 200 years its population has been consistently around only 1500 people, so I'm very interested to hear more about your family.
My great-great grandfather, John Mugford, was born in Bampton c.1818, but there are almost no traces of any Mugfords in Bampton...only Mogfords, so I'm toying with the idea that he may have been born a Mogford and his name inadvertently changed to Mugford when he moved to Plymouth, because he was illiterate.My theory is that prior to 1840s Mogford was the customary spelling in North Devon, and that Mugford was customary in South Devon, so anyone that couldn't spell just adopted the local spelling. This fits the population demographics of the two family names in the 1851 census where there were a multitude of Mugfords in Plymouth and no Mogfords and vice versa in the Bampton/Tiverton area.
Unfortunately, the Bampton church records between 1814-47 are missing, so I've no way of confirming this.However, from the record of his marriage to Susannah Anthony in Plymouth 1849 I managed to find out that his father was called William.
This makes sense because he named first son William Abraham (1844).Your family also has a William and Samuel, which matches mine, but we don't have a Robert however.The other children were: John (c.1848), Richard Henry (1849), George Frederick (1852), Samuel James (1854), Alfred Erwin (1858), and John Thomas (1862).
Please do let me know more about the research you're doing into Bampton Mogfords, and perhaps we'll find an overlap somewhere.