Not having been able to get rid of the timestamps using the method described above, I've come up with an alternative approach:

1. Inspect document, and remove personal information.
2. Check 'Allow this information to be saved in your file.
3. Convert .docx to .zip, and open folder
4. Open 'comments.xml' and 'document.xml' with Notepad++
5. Replace w:author="Author" with w:author=[Your Name]
6. Copy the adjusted xml files back into the zipped folder
7. Re-convert .zip to .docx

This removes any timestamps, but still shows comments and changes under your own name. Of course, if several different people have made tracked changes or comments, it'll remove their names, and put all changes under your own name. But this could be gotten around by comparing files, as suggested in an earlier comment in the thread.