I might be wrong about this, but not being able to set the timestamp is an issue in android, i.e. a limitation. And while Syncthing relies on timestamps (to some extent) and still works, it does so only because it keeps a separate db with the original timestamp data around.
So if the Gallery app relies on the filesystem timestamp (instead of the exif data embedded in the file, which is not affected), you'll be out of luck.
Using syncthing has the benefit of you being able to restore the original timestamps when you backup to your computer, as syncthing will then restore the original timestamp on supported filesystems.