Doubtful? Maybe. Plausible though, plausible. Especially when we are talking about a POD this early in the colonization of North America.
Scotland does not have the population base,
And the Dutch did? You don't need a large population base, just enough space and time; geometric growth will do the rest.
and France didn't have the political will
I think at this point it wouldn't not have the will, either. They'd tried to make the Quebec region a going concern and it was failing. Why not cement the Auld Alliance by being generous with what for France was looking like a bad bet.
so you end up with with a New France sized Nova Scotia instead at best. 70-75,000 by the mid 1700's as opposed to the 11,000 or so OTL and that's based on them having OTL French Acadia minus the Gaspe.
I think the numbers will be higher as they will attract more of the Scottish immigrants instead of having Scots scattered across the British colonies like in OTL. However, even those numbers are enough to give you a viable Scottish colony, which was the OP target.
Everything was by charter at this time. the King granted the charter (essentially a monopoly) to develop the terr. to PRIVATE interests.
Good point. So, someone forms the Scottish West Indies company for James VI to give the grant to. We can add that in.
These were simply not as a rule given away on a whim to a foreign power except as treaty obligation following a war or for a prid pro quo somewhere else.
Well, we can probably find some situation where it would be worth the French while to do so. Or we just have the French colonies fail entirely, and Scotland step into the breach. That happened all the time in this period, and in fact happened to the Scots, here it could just be the reverse; luck played as much of a factor as anything else.
the crown did not bear any responsibility or risk unless they where a shareholder or investor in the development of the colony. the Charter members ( private individuals ) bore all the financial risk and obligations of bringing people to the colony to develop it. James the VI has no reason to deviate from this norm, especially given that his kingdom is rather poor and "financially challenged" shall we say relative to the other colonial powers...At best they have the resources of the Swedes perhaps... Unless the Charter interests fail miserably a few times or, as was the case with the French, the colony will not be taken over by a cash poor Scots King as a direct perogative of the Crown.
Good points that we might want to include in an actual timeline, but none of them deal breakers in my opinion.