Darn...I don't think that's what I was aiming for, either...I'll try to take a closer look and post a picture once I get home.
I'm thinking the issue is the flapper at the bottom of the tank. If I push that down harder, it seems the water stops trickling out. That's what I was trying to get a replacement for...maybe I should save myself some time and just start off posting this in the "DIY blunders" thread?