I now tried copying the contents of the shape while in Word 2010 into a textbox generated in Word 2010. I saved that. When I opened it in Word 2007 those contents were viewable in the textbox but not in the shape.

I then tried, while in Word 2007, selecting the unviewable contents of the shape, copying that, and pasting outside the shape. It then was able to be viewed in Word 2007.