I'll take a look at them and see if I can find something of them in Dutch archives :) Here's a thread also mentioning the Dutch connection
And here's a source, reprint from an ancient book it says : The early history of the Tryon family maybe you already found this one, but just in case ;)
And this one : The Lindgren/Tryon Genealogy: The Ancestry of John Ralph Lindgren and ...Tyron Door J. Ralph Lindgren just search for Tryon here and you can go from there to all pages with info about the Tryon family
And here's the Pieter Tryon and Dutch ones mentioned :
Christoffel (Darther) Gerritsz Tirion (Tierjon), born 1605, died at Rotterdam in 1653, origin from Belgie, possibly Gent, (where in 1585 Pieter Tryon was living a Baptist (his religion), or from the area of Luik, (where maybe the original name would have been Thierry ?), Christoffel married at Rotterdam April1, 1623 Jeanne Antoine. From this marriage (Tirion-Antoine) were born (o.a?) :
1. Isaac Stoffels Tirion, bapt.. Rotterdam 16-2-1628, buried. Gouda 21-12-1699,
2.Jannetje Tirion, married before 1725 Ds. Abraham van Loon, born. Gouda, died before 1725, Baptist Preacher at Dordrecht (1678-1689)
in An act of superscription , wills and opening,at Schiedam
date November 28, 1725 is mentioned Johanna Tierion
widow of late Rev. Abraham van Loon
As you can see the names were written totally different so if you try
and search for them in Holland try Tryon, Tierion, Tiron Tirion Tyrion
And here : Nikhef L. Lapikás, Kwartierstaat Van Schothorst, version 10.1, Muiden, 2014. a whole bunch of others starting with Isaac Stoffels Tirion, too many to translate , but if you would like to add them to the Tryon lineage and/or need stuff translated I or maybe one of our project members would be glad to help of course :)