Im currently searching my family tree which is also Jamieson.
They came from Islay (Argyllshire), Govan (Glasgow), Sunderland (Durham) and Southampton.
Im unsure if any of your family are from any of the above places or it ties into your research but id be happy to share what we have it if will help.
My email is firstname.lastname@example.org
Suzanne & June Dawn nee Jamieson