I understand that this was the home area of the McGregor clan and at some stage in History the English banned the clan and the McGregor name and that families in the area chose to adobt variations such as Gregson and Grierson among other variations.
Where do I start?
Galloway is not, strictly and historically speaking, clan territory. Originally the clans were a social feature of the Highlands, not of the Lowlands and south of Scotland, though the concept of clanship has now spread to the most significant families in the Lowlands and south of Scotland.
The heartlands of Clan Gregor were further north, in Perthshire and Argyll, and there are no records at all of baptisms, marriages or burials of M*cGr*g*rs in the county of Wigtown before 1766. (There is one record of a Grierson in 1706.)
It is true that the surname MacGregor was proscribed, that many MacGregors were forced to change their surnames, and that Grierson and Gregson were among the names adopted.
However this cannot be blamed on the
English government, because the original edict was pronounced by King James VI (who subsequently became King James I of England) in 1603, and was restated by an Act of the
Scottish Parliament in 1617. See
https://en.wikipedia.org/wiki/Clan_GregorOn the other hand, according to G F Black's
The Surnames of Scotland the Griersons of Lag, Dumfries-shire, claim descent from Malcolm, dominus de MacGregor, who died in 1374, but he goes on to say that Col Fergusson's
Lairds of Lag says, 'There is no evidence or foundation for the story that this family was an offshoot of the Highland family of MacGregor'.
There are records of Griersons dating back to the 15th century, mostly from Dumfries and Galloway, so not all Griersons were proscribed MacGregors, and in particular I see no reason to think that your Alexander G was descended from a proscribed MacGregor.
(You could try to blame the banning of tartan and bagpipes among other things after the 1745 Jacobite Rising on the English Government, except that by then the parliaments of Scotland and England were united (1707) so it was the
United Kingdom Parliament that was responsible for that edict.)