Well, I got the gearing figured out. The cable still needs to be replaced since it is kinked and worn from catching on the heron in front, but I moved the shifter further toward the grip and now it doesn't catch anymore. After some lubing with WD40 and some adjustment, the gears seem to be switching predictably.

I keep coming back to this picture:



You can see that the shifter cable is actually looped around the heron. With the shifter closer the grip, it doesn't catch anymore. I'm starting to shine the chrome and most of it looks pretty good underneath, at least the primary hardware (handlebars, brake levers, etc.). The add-ons like the light and the bell.... not so much. But at least things are getting cleaner.