Familiar with the Amsterdam City Archives and the city itself, I started looking for his descendants. Residential addresses, choice of baptismal churches, real estate transactions related to death, etc., I keep puzzling, in the expectation that it will become clear which generation of 'Jeronimus' plays a role in this.
My knowledge of the old script is unfortunately not good enough, I leave that to others.
Also, through a Google search I came across an article from 1985, which deals with a fraud case: 'A Case of Fraud: The Dela Croix Letter and Map of 1634', of which I have included a link at the sources.