I recently acquired a used bike with a coaster brake that buzzes when the wheel is coasting. The brake engages with the expected amount of backpedaling and stops fine, and the clutch engages on forward pedaling just fine, but when the pedals are still, the clutch tends to rub the shell of the hub and make a buzzing noise. There is a very fine interval where you can adjust the pedal position and the noise will disappear, but the default is for the coaster brake to buzz when coasting. The bike itself is only a few years old and looks very lightly ridden (original tires still have lots of tread, paint is fresh, etc)

Things I've tried:
1. Looked at every single coaster brake thread on these forums going back 8 years
2. Read through the following very instructive webpages:
sheldonbrown.com/coaster-brakes.html
http://www.arnettmotorbikes.com/inde...s/Page645.html,
http://www.troubleshooters.com/bicyc...d_overhaul.htm
http://www.parktool.com/blog/repair-...edal-brake-hub
3. I've disassembled the hub, greased everything well (though it was already well-packed with fresh-looking grease), inspected every part for wear or damage, and reassembled it
4. Reassembled the hub without the brake shoes to determine whether it was the shoes or the clutch (it still buzzes without the shoes)
5. Reassembled the hub without the clutch spring to see if the clutch spring was somehow causing the clutch to engage prematurely (it still buzzes without the spring)

I'm totally stumped by this thing. I've ordered new guts for the hub (clutch, spring, and shoes), but I honestly don't see how they'll help.

Any suggestions?