Thank you Hotrod Lincoln. I did verify the wiring on Sunday as I was testing grounds. That all checked out. I did find some exposed wiring at the ignition switch in my inspection. Nothing was loose or corroded. Everything was where it was supposed to be.
This is the second vr that I put on the truck since the problem surfaced. The first was way worse - battery wasn't charging, and voltage output was all over the place. This one is charging the battery. The hum is only for a few seconds on start-up. If it doesn't happen right away, then it happens when I first pump the gas. Again, it stops on it's own after a few seconds, and voltage steadies at about 14 volts.
There is some flickering in the lights, but that levels out as well.
I am picking up a duralast solid state regulator today to see if that changes anything.
Thanks for the feedback.