Actually, I figured out what was going on with Flickr Uploadr.

Seems that if there is an FileModifyDate tag and an XMP tag regarding when the file was modified, Flickr Uploadr apparently used the most recent time. So, not knowing that the XMP tag was there, I was modifying FileModifyDate and it didn't seem to help. Once I used Exiftool to get rid of the XMP tag, my problem was solved.

Thanks again.