This is great information, I really appreciate your help here. I think I follow the logic choosing the resistor value, I was stuck on thinking that they had to match to get the 50/50 duty cycle, but the way you explained it makes sense although I still have a couple points to clarify:
I couldn’t find anything in the datasheet that specifically said anything about the discharge pin’s current capacity or sink current other than a graph that was labelled Discharge low output voltage versus discharge sink current. From the 470R value you came up with that gives me about 6.4mA current at the discharge pin, so it seems by the graph that you were keeping it under 10mA which also shows up as I_DIS in the characteristics table?
This really has me baffled, I think my concept of a transistor is overly simplified, I’m not exactly sure how you arrived at the ~0.7V (and presumably -0.7V) value or how to change it, but a little digging around has led me to Fixed base bias, is that what would help me here?