Stopped at the Verizon store after work. They said they needed to recreate the problem by testing how much charge the battery would take. The total process takes an hour so I declined.
Called the Verizon Warranty Center and the tech instructed me to turn the phone off to charge it overnight. This worked (battery fully charged and working normally) but it's not an acceptable long term solution for me.
My suspicion now is that due to the poor signal strength where I live (the suburbs but apparent Verizon dead zone) the wall charger simply can't overcome the phone's amped-up call standby power consumption.
I am going to do some more investigation when I get home. From what I have read the wall charger is rated for 1A output, however due to cheap construction and cable losses the actual output at the phone could be 0.5A or 0.6A. I also read somewhere that the S3 has a circuit that limits incoming current to 0.9 Amps to avoid battery damage. I am thinking that a better wall adapter and cable might provide more current and give me a full charge overnight.
This still does not explain why the phone says 100% and then instantly drops to 60% when unplugged.