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Mike PeichTrae--This is a great find, and thanks for sharing it with us. I will try and clear up some of the mystery surrounding the overprints based on the research I've done in American printing practices. I should also add that I make books by hand, so I practice what I research and preach.
One of the most expensive elements in any printed object is paper. Pressmen (and they were usually men) were particularly sensitive to this fact and would often use previously printed sheets to check their registration (lining up a sheet so that the colors all fall into place) before beginning a press run. These practice sheets, usually called waste-sheets, had been previously printed and discarded because they may have been used to set up the press, or they may have contained technical errors that rendered them unusable from a quality-control perspective. Before beginning a press run it was important to make certain that the press printed the sheets correctly because once the press was set in motion, a mistake could be replicated many times over before any error was discovered. If an error escaped the pressman's view, a lot of valuable paper would be wasted, and the pressman would be held accountable for the loss of paper.
So, to prevent printing mistakes, and to exercise frugality, pressmen would use waste-sheets to make certain that the press was set up correctly before a press run was begun. In most cases a multiple printed sheet, like the T-206s Trae found, would be discarded because it's difficult to check for errors on any sheet that is printed more than twice. In this case, though, the pressman brought the waste-sheet home, possibly to show his children, and eventually it got into the public domain. (I exercise this same process at the press I operate at my university. The paper my students and I use is very expensive, and I don't want to waste it in setting up the press. This is due to the fact that I don't have much spendable income because I have all these pieces of old printed baseball related cardboard in my home!)
I hope this helps explain what is a very unique example of the printing process. In fact, Trae, I would be happy to add your cards to the trove of examples I use with my students to illustrate early printing practices. You will be performing a great educational service, and I will be a good steward for your cards!
Happy Fourth to all, Mike