Transform, Mesh Filter, Mesh Renderer, tk2dSprite, Mesh Collider.
Of course, now that I've changed the Order in Layer to 1, I can no longer reproduce this on this particular object just by changing it back to 0.
It's still happening to other objects, however, like an animated sprite on the same loading screen, which has Transform, Mesh Renderer, Mesh Filter, tk2dSprite, and tk2dUISpriteAnimator on it. Its Order in Layer goes from 0 to 1003... why? I have no idea. It doesn't happen consistently to all sprites.
I have no explanation for this...