: Summarising -
: As far back as 1391 we find a Petri Caldwell being
: granted the lands of Scottishaw (now called Gaylis)

The Gaylis theory takes a bit of a battering when I find on a Fullarton site that the land of Gaylis was originally granted to a Fullarton by Walter the Steward in 1283 and renewed by Robert II in 1371. This was ok with Sir Adam Fullarton on granting it to Petri Caldwell in 1391 but it doesn't say when the name was changed from Scottishaw. One would think that if the Carta said "formerly called Scottishaw" then the name change would have been in fairly recent memory from 1391. In this case when what is referred to as grants of Gaylis were in fact Scottishaw by its new name. But then how would they know which property was being dealt with? (shrug, puzzled).

On the subject of Colgrieve I have managed to find a facsimile of a many quartered coat of arms on www.achievements.co.uk/tv/revealing.html this is the Colegrave-Manby shield and has been quartered 16 times. The family was from Cann Hall Leytonstone which is now absorbed into north-east London.

The interesting part is that this family seems to have come from the area north of London and possibly from Huntingdon. The shield is quartered with mainly English family name but it also has Caldwell and Fenwick. The Caldwell coat is the English Caldwell coat of arms with the the cross patee fitche and the oriole of stars.
The English Caldwell family has a legend that the family originated in England then went to Scotland then returned again to England. It almost has to be connected with the "Honour of Huntingdon" which was a fief of the Scots Kings in England for centuries.
What I have found is not proof of anything in particular excepting that this particular Colegrave family married into the English Caldwell family. What I would expect to find is that the Colegrave family were named after an estate of that name and that the ancestors of Petri Caldwell (1391) may have had overlordship of it at one time. I still have not found that estate but would expect it to be in the English Midlands within the area bounded by Derby Nottingham Cambridge Northampton (this sounds suspiciously like the Danelaw).