I think that I can say with a good deal of certainty that there was a mass migration of Caldwell families (along with many others from South-West Scotland to Northern Ireland from very late in the reign of Elizabeth I right through to Wiliam of Orange.
As the trip was a relatively short hop and in an area where even a fishing boat would serve to transfer a family and possessions the migration would be largely unrecorded.
Approximately 200 years later conditions in Ireland (famine and religious problems) resulted in a further migration from Ireland to (mainly) North America.
These migrations were almost certainly better recorded and the surviving shipping lists a source of research for students of the name.
The problem is obvious:
Even today, with computers, better ecord keeping, literacy, the internet, and possibly more time (?), we are struggling to trace our families back 200 years!
Consequently the early US families seem to largely come to a stop at the US founding fathers. There is generally knowledge of emigration from Ireland, the prevailing Scots religion, and a surname from South West Scotland (little more). Pretty much what one would expect.
I believe that the Irish records are not particularly good and the Covenanting times in Scotland were also difficult for the process of record keeping.
The thing that I find hard to get my head around is the whole mindset of the struggle for the Covenant. Those supporting it wanted the freedom to chose their own religion mainly based upon how they organised it. They did not see themselves as disloyal in any way but were prepared on many occasions to take up arms to defend it.
It was said of the Western Scots Colliers that they had a system of "negotiation by riot" over their wage demands. Something similar might be said of the supporters of Presbyterianism.
The various kings "of absolute monarchy" (James VI of Scotland to James II of England) saw the Presbyterian idea of the king being subservient to the Church as an abomination. The Kirk wanted a form of constitutional monarchy well before royalty was ready for it.
Royalty and its government saw the Presbyterians as nothing less than out and out religious fanatics, rebels and traitors and treated them as such. This was probably initially much to the surprise of the over zealous Presbyterians but repression, as always, entrenched the attitude of both sides.
The colonisation of Ireland was initially an escape from the conditions in Scotland to an area where they were not being persecuted and the government threw grants of confiscated land about to encourage them. They obviously thought that they would be a buffer to keep the "mad Irish Catholics" in place. It looks a pretty foolish policy from this point of hindsight but it was a continuation of a tradition of government that goes back (at the very least) to William the Conqueror.
Unfortunately it was probably the more extreme factions of the Presbyterians who emigrated to Ireland. This has resulted in sectarian troubles with the Catholic Irish which is yet another sad story. At least this was the most likely source of the subsequent large number of Caldwell's heading for the US fleeing further unrest and violence - merely (still) looking for a peaceable place to live.
There was also another stream of Caldwell immigrants to the US and Canada directly from Scotland - possibly in smaller numbers and submerged in the veritable tide from Ireland.
Finding a line of Caldwell's through Ireland back to Scotland in the early 1600's is a big task and a challenge for us all.
I think it will be necessary to start with known emigrants from Scotland and trace upwards, hoping that the backward tracing will eventually meet.