Yeah, I can't see passive diode clipping being very effective at all. It's whats found in the later stages of a distortion circuit, following an amplifier. The two diodes make a big difference following a powerful signal, but make a very small difference after something like typical guitar pickups. They will also cut your output a bit, as they definitely weaken the gain of a distortion pedal noticeably.
Now if you preamp your guitar and put the diodes in after the preamp, it would make more of an effect.
I would keep looking for the right tone in an overdrive or distortion pedal, though. The sounds in Say it ain't so seem like a nice vintage style overdrive to me. Cut your volume back a third or so in the soft parts, and then crank it for the grungy chorus sounds.
What distortion or overdrive does he use? That would be the best investment you could make, I think.