As @nizantz previously mentioned, using Date.parse() wasn't working for me in Safari. After a bit of research, I learned that the lastDateModified property for the File object has been deprecated, and is no longer supported by Safari. Using the lastModified property of the File object resolved my issues. Sure dislike it when bad info is found online.
Thanks to all who contributed to this post that assisted me in going down the path I needed to learn about my issue. Had it not been for this info, I never would have probably figured out my root issue. Maybe this will help someone else in my similar situation.