It's an interesting theory, anon. But please keep in mind that the Pilgrims landed in Massachusetts Bay in November, 1620:
https://www.plimoth.org/learn/just-kids/homework-help/who-were-pilgrims#:~:text=Arrival%20at%20Plymouth,seek%20shelter%20at%20Cape%20Cod
The King James Bible was published in May, 1611, some 9.5 years previous to the Mayflower's sailing. Your logic seems solid for King James decision to authorize it, however, the dates don't line up. Just sayin'.