I was having a problem with itchy skin. The first thing the doctor asked was if we used Bounce in the dryer?
She also told me to use allergen-free soaps in the wash and on myself, but said Bounce, etc. was a major culprit. A skin specialist I consulted about another problem said the same thing.
The problem has largely abated since we changed our washing habits.

We haven't used Bounce for a year now and don't miss it.

Our dryer has a heat-free setting that we use for fluffing. I notice the lint trap picks up a lot of stuff. The damp towel idea is one we sometimes use when we have dry 30 below weather.

The idea put forth by Bee is worth trying. It also worked for me once, I remember. And with it try slightly misting sections of the blanket in combination with the brushing. The static electricity always is a problem here in the dry winters.

Always check the tape after the first swipe. If it pulls the colored wool of the blanket, stop.