If the slate is going to be buried in the substrate, I would instead use tile. A glass/tile drill bit only costs a few bucks and goes through tile easily. Just slitly score the tile before trying to drill it otherwise you will will just have a dancing drill.
If you want to be able to plant right up to the edge of the wood, use nylon spacers between the tile and the wood. this lets the tile sit on the bottom glass and be covered by a few inches of substrate.