Like Rayjoe in post #23 I've had same experience, when a stiker put in the shield came off it leaved an area clear.
A couple years later my shield became hard to see thru in front of the sun or at night due to incoming headlights, it was full of swirls; so I decided to take all the hard film of it, I used clear packaging tape (Scotch tape) going a little bit at time, applying it and pulling it off, it really takes that hard film off.
Whit a 4 inch cotton buffering disk fitted in my drill, at low speed and "3M Hand Glaze" I polished that shield that looks almost new.
A friend of mine told me about doing this, I just finished it today. Hope this does some help.
Attached is a newspaper seen thru windshield.