I don't see this as a sensory issue, but as a perfectionism issue. My DD7 did/does this, but not quite to that level. But by drawing a line in the sand there, you might be making it worse.
Five is a good time to start transitioning to showers, and that would solve this problem. If your DD is reluctant to try it, you could tell her about how the shower would rinse all those little yucky things down the drain.
Another way to go would be to give her some tools to remove those little fuzzballs herself. That's how I got my DD to relax about spider webs on her outdoor play set. I gave her a magic wand (old scrap of PVC pipe) and showed her how to wave it to make the webs disappear.
