In most cases, mast steps and halyard organizing plates should be attached to the deck with lag screws only, not with substantial backing plate nor nuts. The reason for this is twofold. One, backing isn’t need because the fasteners are loaded only in shear. They are there for the sole purpose of keeping the butt of the mast from sliding sideways. They are not going to hold the mast up if a spreader, shroud, or stay fails
Two, if the mast falls, taking the mast step or plate with it, you want the fasteners to pull out with minimal damage to the mast and deck. If you through bolt a backing plate, a dismasting leaves a big hole in the deck that lets in water and is very difficult to repair.
If the screw is turning, that means the core into which it is fastened is damaged and should be repaired appropriately. There may be core rot in there.
Judy B