Results of the sasines search so far:

1. Glasgow Burgh Register of Sasines
Start in 1694
I searched the first two volumes; 1 November 1694 to 28 November 1701 but no mention of any Sinclair of any spelling or any first name at all.
There were a few John Scotts as follows:-
B10/2/1 1 November 1694 - 29 November 1698
82. John Scott, 3 December 1695
155. John Scott, 10 February 1697
185. John Scott, 18 September 1700
263. John Scott, 15 November 1701
Also several other Scotts mentioned as acquiring land within the Burgh So, I think that indicates that Alexander was not a landowner in the Burgh before his departure for Virginia. I was getting a bit worried because the Burgh sasines were all in Latin in old scots handwriting, so if I had found an entry for him you may have had to wait a while for a Latin is pretty rusty!

2. Glasgow Barony Sasines
Not begun until 1781, predated by Registers of the Great Seal

3. Registers of the Great Seal
The only records available in Glasgow Archives were up to 1651, I will have to search 1651 onwards in the National Archives in Edinburgh. There was nothing directly relevant in the records I looked at, but really they were too early to be of much use. I did find your George Sinclair of Glasgow University and also some records of a Sir John Sinclair of Stevenson (more below).

4. I looked up the Bogle family and found masses of records they were a major mercantile family in Glasgow. Starting with grain import, they then seemed to move onto more profitable exotic commodities;tobacco, sugar, and latterly moved into smelting and engineering. However I was a bit wary about getting bogged down in Bogles at this stage, and wanted to try and stick to Sinclairs. One Bogle entry I found was:-

George Bogle of Daldowie, Virginia merchant, 1701 - 1782, son of Robert Bogle, merchant. Lord Rector of University 1737, 1743, 1747, 1757. Married Anne, daughter of Sir John Sinclair of Stevenston.

This I suspect is the same marriage reference as you found. Stevenson is in East Lothian (miles away from Glasgow!) about 2 miles east of the town of Haddington, and including a place called Pencaitland. It is also fairly close to another important Sinclair seat at Roslin (the Catholic branch), but at present I do not know the relationship (if any)to the Earls of Caithness. I also found a skeleton family tree for this branch of Sinclairs which I will not detail now as we still do not know if this is the correct branch. If you think Anne may have been related to Alexander I will see if there are any family papers for the Sinclairs of Stevenson lodged in the National Archives.

Other possible leads from the Bogle index were :
Bogle (Robert) & Scott
Merchants in London 1769 B10/15/7328

Robert Bogle W India Firm
RC III p128

The Bogle Papers
Bogles of Shettleston & Daldowie
Letters and letterbooks, 1725-31, 1729-42, 1759-61
Including Virginia tobacco trade

Robert Bogle & Co
Owners of the Albany & Scipio trading to Virginia in 1735

From other entries they also appeared to have been involved in East India trading too.

I will leave you to think about this but suggest we finish the sasines first, and if you think there really may be a family relationship between Alexander and Anne I would go for that next. The Bogle trading material may well mention Alexander but might not be much help with his parentage.

Regards for now,