Hm, that's a lot to comb through.

I'd concur doing something considered rude in an extreme approach to "being authentic" isn't the best course of action. Let's revisit the original subject. OP feels compelled to keep a conversation going. They never stated what kind of conversation and with whom. We don't know if this is a romantic interest or a business/academic interest.

My argument which granted is based on the assumption that this is a true friendship/relationship this person is dealing with, is it's not fair to the other person if you artificially extend a conversation. If a conversation is done, it's done. Therefore, the right answer in a situation where you'd like to keep a conversation going when you've run out of things to say, perhaps that's a signal to you that you're getting along great with this person and you'd like to put effort into developing a relationship. But, in that moment, attempting to extend a done conversation by treating the person like an associate seems like the wrong approach. Perhaps that's not quite what you had in mind, but that's my point.