I was thinking you could make the animation flip horizontally when it reaches the last fame, however that would mean you would have to omit #4 and #5 to avoid duplicates, but it still would look odd because frame #3 would skip directly back to frame #0. I tried thinking of different orders the sprite frames could be placed in to clean this up, but all my solutions either result in duplicate frames, or ugly skips. Maybe you might be able to solve what I couldn't.
Unfortunately, it seems that though Godot supports play_backwards functionality for the animation_player node, there is no such feature when it comes to animated_sprite. Too bad, because this would likely solve your problem.
For now, I think your best bet is to do what you were trying to avoid.. flip the sprite images yourself and add them as animation frames, or make a separate animation containing the flipped sprites and have them switch back and forth after their last frames, respectively. It might be a lot of work for super large projects, but without some kind of play_backwards functionality for animated sprites, I don't think it's worth breaking your back trying to find a workaround this time.
Of course, if I am wrong, I would welcome any correction from the community.
Good luck.