IIRC, the four screws go into square nuts that are held in "tracks" integral to the floor. You will need to get under the car to access them. I believe the nuts are M5, and 12 mm on each side. I found them online.
Also, I worked on a car that had its flex disk come apart and the driveshaft mangled the "tracks." I was able to secure the shifter plate with screws and nuts. You need a helper to hold the screw on top while you put the nut on from under the car. Unpleasant job.
WRT your shifter play, you need to replace the bushings in the shifter, especially at the front of the shift rod where it connects to the transmission. Several places online sell a rebuild kit. You will have to pull up some more carpet on the tunnel to access the front bushings which are under a removable plate.
Good luck,
CT