Fix the peaces on the board fill up with liquid rubber or silicon, wait and take it off Warning: i never tried!).
Or take hslfcut Firematches and fix them on the board. May be difficult.
Be aware, that the grid is lower than the tiles.
My first prototyp is with a grid of small sticks, but the tiles are higher.
The man himself! Thank you for the reply. About 30 minutes before I read this post I had the idea of using wooden sticks as a frame for a grid. Good idea about the liquid rubber too, I'll have to do some research.