How the heck do I get the cable runner/guide over the larger round piece. Does it come out if I hit it hard enough? The other side seems like it has a lip that prevents it from coming out. I've come this far but I Feel like I'm failing one of those Chinese Puzzle IQ tests.

Solved. You do just bang out the other end. It's a bushing. I used a lot of things, then a prybar and once it moved a little it started to move a lot.

 

That just all goes back together with the new cable
The serrations on the bolt make it where you have to pound the bolt in there then install, the nut
When assembled and the nut is tight, the cable will still be able to move around as the shoes move around

 

I'm going to answer my own question since I figured it out and someone else might have the same problem.

Once you've pounded the bolt out (the splined bolt), you turn it around and there's a bushing - you can't see it in the photo because it's the opposite side of the round thing that looks like a washer (to the left of the ring of the new cable.

The other side of that makes it clear that thing is a bushing. You pound it out. It's scary because it didn't seem like a bushing, and it took a lot of work. I used a prybar at one point and that got it to move a little, then it was easier. Then you put the ring on and reassemble.

I found that getting the bushing tight was not feasible until I got the unit on and tightened it down using the bolt (the splined bolt) that goes through the hub, tightening down the nut on the inside of the wheel.