Older Drain Overflow Plate Won't Remove

My house was built in 1940...I have no idea if the plumbing is original or not. The bathtub has a slow drain and by slow I mean 4+ hours to drain a 10-15 minute shower. It, of course, was not this slow at first but my husband put it off and now it is really bad... The overflow plate had only one central screw, which we removed and a six sided nut which we loosened but the handle will not come off, so the plate will not come off (it is loosened away from the tub but cannot come out until the handle comes off). Please help, I am a full time student and don't have the money for a plumber!!! Surely this thing is meant to come off...any clues??

a couple additional things... the drain stopper (i believe) is the plunger type, (there is nothing over the actual drain opening in the bottom of the tub) to operate it, you move the handle from one side to another and it is upposed to stop the drain...however that does not work either...it had not ever worked even prior to the slow drain...and keep in mind, everywhere I look on the internet is talking about two screw openings...there was only one central screw...

THANX!

old bath tub

See if one of the local hardware stores would have a handle puller so as to remove the lever handle.
If you're lucky you will be able to pull the guts out of the overflow and there will be a load of hair on the end.
If that doesn't work then you will need to snake out the drain.
And that begs another set of answers.