The fridge is a GE Profile Arctica.

Water connection is braided-steel hose, 20', to the cold-water side of the hot water heater (the nearest cold water source).

I've been using inline water filters for a few years, and the bypass insert for the in-fridge filter.

Within the past couple of years, we noticed white "stuff" floating in melted ice cubes. The water from the dispenser is (and has always been) crystal clear and clean.

On the advice of a maintenance person, we replaced the ice maker to no avail.

On the advice of another maint person, I replaced the feed hose, went back to the (expensive) in-fridge filter, replaced the water tank in the fridge, and the internal plumbing.

In total, I've spent about $600, and I still have white fibrous material floating in my melted ice cubes.

Is there another water tank that might not have been replaced? Is there a hose that I should look at replacing? How do I get to it?

I'm desperate. Any help would be greatly appreciated.