Actually, you do not have to disassemble the unit just yet. To flush out the reservoir does not require any disassembly, merely use a large pitcher at the water dispenser in front to run at least a gallon or 2 of water thru after you change the line from the wall. If you have a filter bypass plug, use it when you do the flushing to ensure the best water pressure thru the reservoir.
If you use your head for a moment, it will become clear why the ice is not affected by floaties, yet the water tank is:
Water for the ice goes straight from the wall thru the filter into the icemaker mold. It does not stay in the drinking water reservoir in the FF section at all...in fact, the tank is never disturbed for icemaker operation. Herein lies the problem....water that is in the plastic tank has already passed thru the filter, so it has been de-clorinated. From there, it stays in the tanks for a day or three, especially if you do not draw copious amounts of cold water every day to flush it out. The de-clorinated water sitting in the tank will cause precipitates, floaties if you will. This is enhanced by the vinyl hose on back that we have found out causes taste and odor issues already.
I found this out after hundreds of service complaints while I was with MCS, and it was only after experimenting with replacing water tanks and finally swapping out those soft hoses for hard copper that finally did the trick. It turns out that filtered water leaves the tank open to organic growth. Even though the white precipitate is not pathogenic, it still is disturbing to see in a glass of supposedly pure water. So, changing out the water line and thouroghly flushing the tank by running a gallon of water thru it should do the trick. If not, then you can go poking around in there and change the tank itself.