[SOLVED!] (via another forum post of mine - Unable to Upload Sketches to Arduino on Breadboard ATMega328P-PU Using a FT232R - Programming Questions - Arduino Forum)
I was able to get both my FT232R and my CP2102 modules to work! The problem came down to the capacitor I was using and how I had it connected to my Breaduino.
I still currently have to perform a manual reset in order to upload sketches, but at least I am able to upload sketches.