Bathtub stopper

[Desparatefordrainage]

I have a bathtub drain clogged with hair. Once I remove the little top to reveal a big brass screw I can’t for the life of me get this thing unscrewed. It’s either torqued way too tight for me to get loose or there is something I’m missing. There is no little screw under the stopper and I have tried turning both directions with the stopper up and the stopper down. My hands are sore from gripping the screwdriver and I am likely damaging the brass screw by it slipping off and chipping it. I will try the little plastic snake thing but of all the years of cleaning out my bathtub drains this is the first that I can’t figure out. Any suggestions please?????

 

[CT-18]

Maybe easier to understand with some pictures.