I like the idea and what I'm mentioning isn't quite as good, but it's something to tide you over.
When you're viewing a synth, you can use the fullstop [.] and comma [,] keys to move forward and backwards through the photos according to their original filenames.
This means that if the names of the files were in chronological order before you uploaded them, you can traverse the photos in chronological order by repeatedly pressing the fullstop key.
Being able to sort by EXIF Date data, however, would be much more ideal, as well as being able to edit the date metadata after the photos are uploaded, in cases of a camera's clock being set incorrectly at the time of capture, scanned photos which have no EXIF date, photos from cameras carried across time zones, etc.