About waves versus particles I have little to contribute, but I definitely agree that a key concept is the curvature of space effected by a massive object. The two-dimensional analogies of a bowling ball deforming the space on a mattress are quite compelling in this regard. "Geometrodynamics" is the term popularized by John Archibald Wheeler and Charles Misener in the sixties, where all gravitational effects are attributed to curvature of space and there is in fact no "matter" left at all.
I agree that no usual topological deformations can send an orientation-preserving path to one that reverses orientation, but there is another more drastic transformation associated with the formation of "wormholes" where a tendril from one part of space becomes attached to another part, forming a sort of bridge. There are two ways that such an attachment can take place, and it is not inconceivable that the bridge might introduce some non-orientability where none existed before. Is that a helpful thought on this topic?