Thanks Nigel and Frances for taking the time to consider these points for me again.
I'm inclined to go along with the idea that the name was a local one that evolved into Corjeag and then anglicised to Cavendish - either by the clergy record-keepers or by individuals for the sake of conforming to trends.
Perhaps if I ever get the time and opportunity to study property records closely I'll find an early example of Cavendish there that will give me a different angle. Or if I get to the museum library again, they might, if I'm lucky, let me look at the actual original register to see for myself what the early entries really were.
I know there are some who would like to be connected to the aristocratic English family, but that doesn't include me. I would like to get close to certainty, either way, though.