Oddly enough, after replacing the compressor start relay, I haven't heard the noise since. The old relay was definitely bad, it failed the shake test miserably with little bits falling out. I actually heard the noise the very first time I plugged in the fridge upon putting in the new relay but after that, no more clicking/rattling so far. Fingers crossed. :confused:

After doing more research and finding a few posts on various blogs on the symptom, I decided to try replacing the Refrigerator adaptive defrost control kit (23). It has been about two weeks and I've had no issues. It appears to be fixed. Hope this will help someone down the road.