The timeline

Here’s the timeline clarifying our point:

Early Sixteenth Century—Erasmus and the Foundation

Erasmus located a few late manuscripts in July 1515 and rushed his Greek New Testament to press in October 1515, completing it by March 1516.[1] He produced four succeeding improved editions in 1519, 1522, 1527, and 1535.[1] Erasmus’ text became the basis for the Textus Receptus (“the text received by all”), which became the standard Greek text for the next several centuries.[2]

Mid-Sixteenth Century—Standardization

Theodore Beza produced nine editions of the Textus Receptus between 1565 and 1604.[3] These editions solidified Erasmus’s work as the dominant Greek text.

Early Seventeenth Century—The King James Version

Tyndale’s translation became the foundation for the King James Version (1611).[2] The KJV translators had the Beza edition of 1589 as well as the Estienne edition of 1550 available.[3]

The Westminster Assembly (1643–1649)

The Assembly met nearly a century after Erasmus’s original work, yet decades after the KJV’s publication, and roughly a century after Beza’s editions had standardized the Textus Receptus. Crucially, the King James Version became the most popular English translation in the seventeenth and eighteenth centuries and acquired the stature of becoming the standard English Bible[4]—a status that developed after the Assembly’s work, not before.

Later Developments—Displacement of the Textus Receptus

Around 1700 John Mill produced an improved Textus Receptus, and in the 1730s Johannes Albert Bengel published a text that deviated from the Textus Receptus according to the evidence of earlier manuscripts.[4] Brooke Westcott and Fenton Hort worked together for twenty-eight years to produce The New Testament in the Original Greek (1881), which became the standard text responsible for dethroning the Textus Receptus.[4]

Your point stands: the Westminster divines were articulating a doctrine of providence applicable to the entire textual tradition, not prophesying the KJV’s supremacy.

[1] Edward D. Andrews, How to Study Your Bible: Rightly Handling the Word of God (Cambridge, OH: Christian Publishing House, 2017). [See here, here.]
[2] Amy Anderson and Wendy Widder, Textual Criticism of the Bible, ed. Douglas Mangum, Lexham Methods Series (Bellingham, WA: Lexham Press, 2018), 119.
[3] Elliot Ritzema and S. Michael Kraeger, “Textus Receptus,” in The Lexham Bible Dictionary, ed. John D. Barry et al. (Bellingham, WA: Lexham Press, 2016). [See here, here.]
[4] Philip Wesley Comfort, ed., The Origin of the Bible (Carol Stream, IL: Tyndale, 2004), 281, 283.