I seem to have found the solution and want to update in case anyone else runs into this.
I was able to to successfully publish to HTML5 only after I DELETED all of the GIFs that were currently in my library and then reinserted them. Once I deleted the GIFs from my Captivate Library and then reinserted by clicking the Insert -> Animation menu option, I published as HTML5 and my GIFs were intact.
Please note that I had completely replaced all of my GIFs using the Insert-> Animation menu option before (in place of dragging and dropping) and this did not fix the problem. This only worked AFTER I deleted all the GIFs first.
Thanks!