I'm watching the eastwards drift of this thread with interest to see if there may be any possible link with the Carvers of Norfolk (from whom I am descended). In Isleham, Cambs where I live, there is only one Carver record in the parish registers - Robert Carver from Barton who married here in 1697. Barton is not far from Melbourn and Isleham is not far from Barton, nor importantly, from Norfolk, which is less than 10 miles away.
Of course this could all be a complete coincidence, but it still interests me to watch what's going on. I think that my branch of the Carver family take their name from the old English word that means 'ploughman' or suchlike, rather than the more obvious wood carver. There is a family farm in Norfolk and a wood named Carvers Carr.