The following is simply a reply to the question on "There-being," but refused to be posted as a mere comment. Anyway, I hope it's helpful. More in class:
Richardson notes in an easy to overlook footnote on p. 34 that "There-being" is the way he chooses to render "Dasein." So based on our short discussion last time of the "Da" in Dasein (see also Gadamer, top of 23, and Ryan's post)as signifying the way human being IS in the world, as an event or happening, and recognizing that "there" correlates" with "da" in the German, we perhaps can see what Richardson is getting at.
As we pursue our understanding of this difficult concept of Dasein or There-being, we might ask ourselves, in what way is human being most existentially THERE, most present as who we are?
Hang in there!