After many years of research it appears the name was German. The area northeast of London is called East Anglia and contains Norfolk Co. During 7th Century that land was given by the King of England to Saxons from along the Rhine River to try to protect England from the Vikings. The name along the Rhine River is spelled Grauel and many Germans by the name came to America in the 17th and 18th centuries.
John Crowe was in Massachusetts by 1635 but the name in the next generations was Crowell and Croel, etc. and he was called alias John Crowell.
There was an area in Norfolk called Crowland pronounced with the long O. It would be quite natural for those people to spread out of East Anglia and to the rest of the British Isles.
I can not help you with your Scots and Irish research, but thought you might be interested in this information.
I found the Crowl Name Association in America in 1984 and wrote our first newsletter in March of 1985 which still continues quarterly. We have recently started a DNA project to answer genealogical questions which have not been answered by traditional research. See www.Crowlconnections.com
. Best of luck with your research