Since it sounds like you are washing a large amount, but what I do is put the smaller pieces in mesh bags (I have a few large ones) and I also bought a cheap salad spinner that I keep in my sewing room, so if I have small pieces like a charm pack that is what I use. Just a small amount of Woollite to help the chemicals release from the fabric then rinse it well, then spin it to get a lot of water out. I don't always put it in the dryer but if I do I use the mesh bags.
I can relate to your problem, it happens to me too. It took me forever to figure it out. I thought it was the paper we used at work and after reading the newspaper. It seemed to come and go, then it started more when I got deeper into quilting (before I did embroidery with unwashed fabric) and the condition was more constant. Hope the washing solves your problem.