The itinerary you suggest makes the most sense: IAD-AMS and then the train to Eindhoven. KL biz class is good.
Depending on the day and time, you may want to buy a 1st class train ticket Schiphol - Eindhoven, as trains in Holland can sometimes be a zoo (during peak travel hours). Buy it when you arrive, no need to pay the huge fees of 3rd party websites.