Actually those appear to be the very last generation of the Model Six which did indeed use vinyl contact paper over MDF. The very last ones used foam surrounds instead of cloth, so if yours are the foam style surrounds check and make sure that they aren't rotted (foam surrounds from that era are almost always rotted through and you can push your finger right through them).
With all KLH speakers from that era it's recommended to replace the capacitors regardless of whether the tweeters are working or not. The capacitors that KLH used were very prone to value drift and failure, and new caps are cheap and easy to install plus they'll restore your high frequencies to the original spec.