Well, the slight hiss continued to occur regularly even after I had entirely disconnected the modulator and wiring. I'd be curious to see if someone else duplicates this with a stock set up. If not, then it might be an indication that I have somehow damaged my radio.

If I open the driver's door after the car has been sitting for a while, I can hear it. You have to have your ear up against the small door speaker and little background noise, but it's noticeable.