A few corrections - the road at that time was to Linlithgow/Glasgow and it crossed the WATER OF LEITH. The old bridge, which is still there, was built c18.
In 1745 there was a skirmish during the Jacobite Rising known as "The Canter o' Coltbrig". Simply a detachment of dragoons were spied upon by some men from Prince Charles's troops, a few shots were fired by them, and the detachment of dragoons, without returning fire, fled along the Lang Dykes (modern day Princes Street). All in broad day light in the middle of the afternoon.
There was a "Big House" but I have no knowledge of ownership prior to 1810 when Coltbridge House was purchased by Robert Paterson whose wife's mother was a Lindsay and a headstone for her grandparents can be seen at
http://www.flickr.com/photos/7768812@N06/1550385165/sizes/l/ .
Nothing to do with Greig but it fills in the evening.