Not knowing who the manufacturer is, limits my knowledge of your slates' assembly process. Some backing is screwed in place & some backing is glued on. Some backing is real wood (most likely poplar) some is MDF or other similar wood particle material. If it is real wood, you might want to have the backing plates planed to insure the plates are all the same thickness, before completing the assembly.
If I were going to replace my backing plates, I would choose Poplar. You might even go as far as to apply a sealer coat, to prevent moisture from being absorbed over time.
I used a biscuit cutter to join my backing plates at the corners. Simple process
There may be books around to describe all the processes & tips in putting a Pool Table together.