The strategy is simple: The courts will declare ‘natural born citizen’ to mean entitled to citizenship by birth with no further action required. The courts will hold that the only other citizenship is ‘naturalized’. The original intent and meaning matter no more here than they do for the ‘general welfare’ clause.
Hopefully, the SCOTUS would not be so obtuse. They need to address "citizenship by birth" (based on bloodline) compared to "citizenship at birth" (based on operation of law/grant of the Sovereign).
And they need to address how dual citizenship by birth (bloodline) may or may not affect eligibility. Surely if someone had told Ben Franklin in 1788 that the son of a subject of the British Crown could be President of the United States, he would have taken out his horsewhip.