Got it. So is it safe to assume the starter is grinding for those 6 to 7 seconds the engine runs with the key in START?

On to trying to solve this problem. The ballast resistor is a long length of wire bundled in the dash harness. When the key is placed in START, full battery voltage is applied to the ignition coil. When the key is returned to RUN, the coil is powered through the ballast resistor wire instead. Between the lowered battery voltage during cranking (key in START), and the voltage drop of the ballast resistor with the starter let off and battery voltage back up (key in RUN), the voltage at the coil stays relatively constant regardless of whether the key is in START or RUN.

You can effectively measure the ballast resistance by looking at the voltage divider at the coil. Turn the key to RUN and verify that you still have 12 volts at the coil. Now manually force the points closed (or short across them). The voltage at the coil should drop to about 6 volts. Just be careful when you let them open (you may get a spark). This indirectly measures the resistance of the ballast without having to probe at both ends with your multimeter.