1. I want to save to the latest format (with no Compatibility Mode) because Microsoft stated that:
"You can work in Compatibility Mode or you can convert your document to the Word 2013 file format."
"Converting your document lets you access the new and enhanced features in Word 2013."

2. I found a way to remove Compatibility Mode from docx files using Graham's converter.

3. I found a way to preserve date/time stamps in the process.

So, the main problem is using Graham's converter with 2013 x64.