Update: Problem solved!!! I went back to the Verizon store to talk to some techs there about it. They had never heard of the problem before and were shocked to see the phone blank out using the method I described to you
earlier. The store manager, who also owns a droid, came and talked to me. We did the test with his personal device and the phone
never blanked out. Also tried a brand new droid with no problems. He figures there are defective sensors out there causing the problem.
They swapped me with a new droid, synced everything back to the phone. This is important to note, because the new device was set up with the
exact same applications, settings, everything. It was identical to my phone in every way except for the new hardware. I took it outside for a quick test and didn't have the problem! Woo hoo! To me, this confirms absolutely that the sensor in my old device was defective. They're going to send the old one back for testing and hopefully improve quality control of the proximity sensors.
In short, if you are having the same problem and none of the other suggestions work (remove certain apps, auto bright control etc), then your sensor is defective! Take it back and get a new one!
Cheers