Alright, I'm on Phase II of the test..."The Re-Charge"
I did what the instructions said, and I had my battery at 100%, which I then killed to ~1% until it shut off. The phone is now turned off, and charging.
In the past, when I would charge it to get it to show 100%, and dis-charge so that it would shut off, it would never fully charge to show 100%; it would stop at 90% when the phone was off, and between 90-95% when the phone was on. We'll see if this is a permanent fix in a few hours when we commence Phase III..."Profit."
Phone: Galaxy S4 (32GB [AT&T])
ROM: Stock, Rooted