Good thoughts on symmetric versus asymmetric verb phrases. You can get yourself into trouble getting too creative trying to come up with the “other direction verb phrase”. In this particular model, I think it may be cleaner to leave some of the verb phrases off. Choose the direction of traversal and provide that verb phrase only.
My favorite example of multiple verb phrases deals with the relationship(s) between “car” and “person”. A rel-phrase combination “owns”/”transports” is just such a problem. I own the car in my garage, but my rental transports me. So, there would be 2 separate associations to link 2 separate instances of “car”.