There were no other children to our Jan - only the daughter born after he died.
When the daughter married the newspaper had her as "the only child of the late John Ver Beck of Amsterdam." The paper then noted "Batavian and Amsterdam papers please copy." Perhaps he spent some time in Batavia before coming to the Australian goldfields.
It is a puzzle but at least you have narrowed it down to a few prospects and we are grateful for that help - before your search it was a complete blank for us.