I do not know if the Pieter Marcelis/Marselis/Marsalis lines are direct descendants of Gabriel or not. Right now I would just be thrilled to find the marriage or birth of John and Prudence LNU Marselis/Marseilles and Mary Gordon Marsalis' verified parentage.
However I do want to comment on a couple things.
The Dutch did not have surnames back in the 1600s as we know them today. Also surnames like Marcelis were usually phonetically interpreted, hence the spelling variants.
Sometimes a place or occupation was added with "van" and in America became the surname.
The most common Dutch naming custom was that of patronymics, or identification of an individual based on the father's name.
The patronymic for males or sons was formed by adding -se, -sen, or -szen.
Thus Marcelis Pieterse simply adopted a common usage. He was a Marcelis "of" or "by"his father Pieter Marcelis. Common meaning for the "se" was "of" . Later at the baptism of one of his children he was called Merselis Pietersen. So again he was the son of Pieter.
"The Dutch were much slower than the English in adopting surnames as we know them. Patronymics ended theoretically under English rule in 1687 with the advent of surnames, but not everyone followed the new guidelines. In the Netherlands, patronymics ended mostly (especially Friesland) during the Napoleantic period around 1811 when everyone had to register and select a family name."
(Some feel that a couple of the children listed as Pieters were actually his son Marcelis Pieterse's children.(A couple of them were not listed above) Hessel Pieterse is also thought by later researchers to be the son of some one else entirely.)
Btw, I have been going back over copies of original records at the Archives and online and cannot find "van" used anywhere as in van Marselis etc for our family though I have read it on trees and been told by others. Later I will post all the original mentions of Pieter that I have found. I give thanks in a big way to the colossal work of Tempe Fenn Crosby and the Internet.