I had the same problem with a threaded in screen on a '28 Model A. But had a '29 Tudor that it unscrewed no problem.
Sorry that is not an answer to your problem, but I am interested in someone chiming in about this.
The four-tab on our '30 Roadster is a breeze to pop out. Maybe why Ford went to that type
I suppose maybe spraying it down with something like PB Blaster may help?? Has to be some old gasoline varnish hanging it up. Like I said our '29 Tudor was no problem. It had an original screen, maybe the one you are fighting is a re-pop from the glorious '70's world of bad parts.