Having humbly begged my Food-Taster for further information, I have discovered that it is only in special cases that he (or, it seems, any other TA) can do this! As he used to work for BA, he has some kind of 'access code' that enables him to override the normally blocked seats pre-90 days (for BA trips). Other TAs may (or may not) have similar access codes for various airlines that offer them "favoured status."
But I still think you should be able to select seats at the time of booking (however far in advance that should be) if you're in l/h business class! But maybe either (a) I am mis-remembering the relevant time interval for the (personal) case I was thinking of or (b) maybe it's a privilege extened to FB Elites in biz!
OP: Did you book on the KL website? Are you FB (or other SkyTeam) Elite or Elite+? (Assuming your JFK-AMS flight is with KL.)
-- Henry