Travis,
That is definitely not a Custom Shop made Model 64. The stock configuration is not Winchester work, and the grip cap on the pistol grip is definitely not right. All grip caps were made of black hard rubber, and have the Winchester logo on them. The screw in the center of the grip caps was decoratively engraved.
One thing that really concerns me, is that I know for a fact that Warren Newman (the CFM Curator) would not have asked or offered to look at the gun, as it is expressly forbidden by Museum policy (and stated as such on their web page). As an infrequent part time volunteer at the CFM, I am fully aware of the rules that they must follow.
Lastly, I just recently finished an in-depth article specifically about the Model 64 that will be published in the Winter edition of the "Winchester Collector" magazine, and I am a subject matter expert on them. In that regard, I can tell you that the rifle is not factory original or Custom Shop built.
Bert H.