Well, it's fixed now. When I installed the new tank kit, I routed the thin little hose down the overflow pipe. The hose was so long, that it went down into the water in the tank and was blowing bubbles. The flapper was coated in bubbles which lifted it slightly (I'm guessing). I cut about 5" off the hose so the end is above the water in the overflow tube and now the toilet works great! Thanks for the suggestions though.