<< I had to jump start the car and when I did, the battery read 12.27 volts. I revved the engine and the voltage went to 12.67 and dropped down a little when I stopped revving. To me that says the alternator is working. >>

That alternator is NOT working properly. Voltage while the engine running with a good battery, should be aprox 13.8 / 14.2 volts. 12.6 volts shut off.