I agree that the Canterbury name is English. There are several stories about how the Canterbury families originated in the USA. It is likely there is some true to all of them, but as you know, right now the stories don't match and there are so many files about the Canterburys missing from the 1700's, it is difficult to tell how the Canterburys are related.
Awhile ago several Canterbury males volunteered to have their Y-chromosome DNA tested. They came from the John Canterbury/Nancy Lowe line, the Jedithen Canterbury line, and the Asa Canterbury line from Illinois. The Y-chromosomes tests all matched exactly indicating there is a possibility that all of these Canterburys are directly related. The John Canterbury line is thought to have originated in Virginia in the 1600's in the Prince William and Fairfax County area. My Asa Canterbury line originated from Fairfax County, VA. Personnally, I suspect they are all one big family.
It is certainly possible that the common ancester goes back a thousand years in Britain, and there are all sorts of possible links with so much information missing. I have also found that in tracing my family, that the origin of the wives are remembered and attributed to the male line. For example, it has been published for one of my family lines the the surname male came from Wales, but documents show that it was his mother who came from Wales and the surname male was born in Philadelphia. So there was truth to the story, but it was not quite right.
By the way, which Canterbury lines do you come from?
I would be interested in learnig more about the Canterburys coming from Dumfries, Scotland. It is also possible that Dumfries was a popular port of exit from Britain. My opinion is we all come from one big Canterbury family originating from Fairfax County, VA, and the male line was originally English. The DNA testing is consistent with this, but does not prove this. There are many other possibilities right now.