You can not use the the paper certificate but you still have a FAA certificate. I found this note on the FAA web site about exchanging the the paper for the plastic -
NOTE
*If your airman certificate or special purpose pilot authorization was or will be issued on the basis of on a foreign license you must first apply for a verification of the authenticity of your foreign license.**You may visit our website for more information and to obtain the verification form.**Your foreign license must first be verified with the CAA prior to making application with the IFO or FSDO to replace your paper pilot certificate or to apply for an airman certificate or rating.**
Did your Dutch CAA license evolve into the JAA? (I don't know know how that happened over there.) If the Dutch CAA can say Mr. Punk has this JAA license which was this Dutch license that you (the FAA) based his license on, I would think it would just be a paper shuffling exercise. You are not adding to your certificate or flying a plane at this point. All you legally need to be current would be a flight review which isn't training or a check ride so I don't know how the TSA looks at that for a foreign national.