I’m going to skip over the third group – the names connected with Cunetio/Kennet(t) in Wiltshire: they confirm the survival in the Cunet– derivatives of the syllable between the n and the t, thus making Countisbury a ‘deviant’ form if it derives from a similar source.
Checking Rivett and Smith’s The Place-Names of Roman Britain I see that an Old Celtic word Cóndate gave its name to a number of place-names, mostly in France (accent indicates the Gaulish stressed vowel) – though it was also the Roman name for Northwich.
The meaning was ‘confluence’ – meeting of the waters: Northwich is at the confluence of the rivers Dane and Weaver. So, could the first syllable of DB Contesberie be connected? The Wind Hill promontory fort stands above the point where the West Lyn meets the East Lyn just outside Lynmouth.
The Historical Gazetteer of England’s Place-names gives twelve variant spellings, among which is 1238 Cundeburye, found in the Devon Feet of Fines. Condatis was a god of the ‘watersmeet’, associated by the Romans with Mars. Countisbury = Cóndatisburh/Condesburh? The odds are a bit against it. In fact, rather a lot against it … But still …