I think that calling these coins 1964 Special Mint Set coins is a serious misnomer and a disservice to the hobby. This 'name' is causing the belief among inexperienced collectors that they can find examples of them out in the world.
1964 Special Mint Sets do not exist and never existed. The coins, at the very best. are Specimen strikes, but no one has been able to say exactly what was done differently to the dies or the planchets. The best I have been able to get out of anyone is a Justice Potter Stewart imitation of "I know it when I see it!"
It could be they were test strikes for the SMS to come in 1965, BUT THERE IS ZERO DOCUMENTATION OF THIS, it is just an idea of mine that would make sense.
I think they are most likely first or early strikes on new dies, that MAY or MAY NOT have been struck with different pressure, that were kept by Ms. Adams in here personal collections. I would presume she would have paid face value for them to keep things legal.
One of the things that people willingly forget is that claims need to be backed up. Claims with no proof are prevalent in numismatics. This causes much confusion and unnecessary frustration and sometimes takes generations to straighten out. In every other professional historical research all claims need to be verified. Just as an example my wife has. through a popular .com has traced her ancestry back to 1608 and found in 1640 something her 6th or 7th great grandfather married an original Fille du Roi. She can join a group similar to Daughters of the Revolution when she proves her lineage by accepted research, they do not accept the popular internet company as they are not known to be, shall we say, accurate in their conclusions. The blind following of numismatists who are accepted as experts has caused enough problems that we should know better.