I decide to go the soldering route. Sure enough, when I stripped a 1/4 inch of insulation from the bottom of the positive battery lead I found many wires broken and corroded.

I solved the problem with my propane torch and lots of solder. I covered the exposed 3/4 of wire below the terminal with solder and heated it well enough that the solder flowed into every space between the wires and within the terminal as well. I then taped it up well enough that it won't be exposed to the elements.

After I started the engine up, I verified 14.1 volts at the battery positive terminal and 14.1 volts at the alternator output as well -- no longer a voltage drop between the two. Hopefully this repair will last another 10 years like the original wire did.