After looking at my planter, I've decided on another avenue. I am going to remove the stakes from the bottom of the planter and cover all the wood in a plastic liner, so none of the soil is touching any part of the wood. I can then just sit the planter on top of the undersoil and fill it with proper growing soil.

This should allow me to grow produce without the threat of harmful contaminants and will also save me having to buy more wood and make another planter!