Well, I tried a few things on the stem, but nothing I can seem to do will reduce the whistle. I made it better by filing the edge down and now it does it only when the bowl gets about halfway down or when lighting, but the rest of the time, I don't really notice it.
I contacted Smoking Pipes to see if they had any of the Peterson stems in stock at all, but it doesn't look like it. Was told I could send it in for repair and it would cost me $40 or have them send it to Peterson for $80, but I only paid a little over $100 for it. At that, I could just buy a whole new one and have two bowls with one stem that worked between them.
I reckon I'm just going to have a whistling pipe. Of course, I could make it my car pipe. Didn't notice the whistle one bit last night on the ride home from work with the radio turned up.