If those numbers are right, you may need no more than a finer filter - like a handful of DE in the skimmer.
Your numbers are pretty much textbook spot-on, and you are evidently able to maintain 15 on chlorine, so I'm thinking that you do not have a problem with anything that is using up chlorine. You are at the proper shock level according to the 'best guess' chart. So, unless the polyquat is doing something odd with the chlorine, it doesn't seem to me that you are needing to kill anything in your pool.

That leaves me thinking that your 'dust' is simply brushing into suspension, passing through the filter, then settling back whence it came.

I'll be seriously curious to hear more learned opinions than mine on this one.