Hi. I am Dutch. I did the TransAm route in 2009 and met many helpful Americans. It is nice to give some help in return.
The Netherlands has a very dense netwerk of bike roads or quiet rural roads. To prevent that you have to consult the maps very often, you better select a few
"Landelijke Fietsroutes" (national bike paths). It is easy to follow the LF sign boards. Set your cursor on the LF number on the map in the following link and you see it highlightedhttp://www.landelijkefietsroutes.nl/routes/
From Haarlem to Urk you might pass via Alkmaar to follow LF15 - Boerenland (Farmers land).
From Urk to Arnhem you follow LF3 - Hanzeroute
From Arnhem to Maastricht, follow LF4 - Maasroute.
A bike route from Maastricht to Luxemburg and Trier you will find in the guide "Onbegrensd Fietsen deel 1a - Maastricht - Luxemburg - Nancy" (last book on the page): http://www.opdefiets.net/fietsgidsen/nederland.htm
I do not know if this route enters Liege, but this is certainly a very worthwhile place to visit. They have a new, spectacularly beautiful railway station designed by Santiago Calatrava.
I guess between Trier and Koblenz you can't go wrong by following the Moselle/Mosel.