I have sent a message to our Toronto researcher for clarification on the inclusion of William from Minnigaf. If I recall this was based on word of mouth thru the family as there is little other than the Bryce Burgess Millar baptism reference to "William of Minigaff" (I must admit that is quite a distance from Dumfries and Caelaverock...but not too far to rule out.). Otherwise we have no idea if he died prior to the 1841 Census, is hiding or has moved elsewhere in the British Domain. If you note my initial post refers to the tentative nature of this relative. My hope is that perhaps some other researcher into Burgess and the KKD/Dumfries history may click on something more concrete.
The samples you found of William's born around that time could be right as well and thus put William as possible cousin to our John b 1794. Perhaps the parent James Millar is connected to Janet Stoba's John Millar. This would push the possible connection back a generation.
Agnes McMichael's marriage to James Dargavel in 1843 and Bryce's rearing by her parents shows that her relationship with William was not enduring for whatever reason. The naming of Bryce by the birth father's surname is indicative of something above a casual encounter I would think. My experience with contemporary Millar's shows a desire to hide such indiscretions at all cost.

We are also at a loss as to what became of Blacksmith John Millar b 1794 Caerlaverock. There was a notice to creditors in around 1860 but we are unsure whether he died about then or just liquidated because he and wife Margaret were off to join their children in Canada. Margaret Millar (nee Francis) did show up alone in the 1881 Canada Census with her youngest son David in Muskoka, and she died around 1887 and is buried on the homestead there.
Hope that helps to explain things so far. (Got the clarification and am PMing you)
rlheco