Sorry that it has taken so long to reply, I forgot my password and it took a while to get it from the web site. Like most geneologies that date back 300 years, there are a number of versions on Jan Jansen.In my "version", I tried to resolve the inconsistencies between the other versions and the timeline.
Also, the book, Pirate Utopias, has information on Jan Jansen.Whether he ever visited his son in America is unsubstantiated speculation, but Anthony did seem to have enough money to be a rather wealth landowner, holding several properties in New Amsterdam.
Another book that might interest you is an historical novel about Anthony's wife called The Drowning Room.
If I come across more of my reference material, I will pass it along to you.