The flapper fixed the problem for a short while, but ultimately the slow leak resurfaced. I went back to Duff's to readdress. The guy at the counter suggested that it may not be a flapper problem at all. Instead, he suggested that the problem might be a siphoning issue. Pretty cool, right? Well this time, he was spot on.
If you notice in the picture below, there is a black tube that extends from the flushmaster down into the white overflow pipe?
This tube cannot be too long. If it extends too far down the overflow pipe (white pipe pictured), then siphoning can occur.
I used a household scissors and clipped the tube and now finally the problem is officially corrected.