I found something in Discovery that may call for a rethink:
1441 Deed of entail: Henry Bradeleygh, Jas.Craas and Rich. Osbarne to William Twynyho (son of John T.) and wife Ankarete: all lands, etc. in Frome Braunche, Little Cayvere and Tuddryngton in the hundred of Frome. 10 Sep. 20 Hen.VI
https://discovery.nationalarchives.gov.uk/details/r/357f0a97-0e6c-42a5-b26a-47a607ca8600
If William Twynyho was already married to Ankaret in 1441, then that might mean that there is one too many Williams, and Codrington/Cobington has to be moved elsewhere.
Something like this:
William Twynyho, of Frome, 1360-1412, married Alice (William's will)
John Twynyho, of Cayford, Frome, and of Bristol, 1390-1444, married Joan (co-executrix of John's will, together with William)
William Twynyho, of Cayford, born about 1420, son of John (Common Pleas and TNA Discovery), Ankeret Hawkeston. John Twynyho the MP is his younger brother, born about 1430-40. In his will of 1485, John Twynyho of Cirencester mentions wife Eleanor, nieces Martha, Edith Lynde, nephews John, William, and daughter Dorothy, which mostly matches the Visitation of Somerset.