Perhaps I’m late jumping on so please forgive. I also suggest using some joint or spackle compound to fill in the gaps. To secure the foam to wood, I used liquid nails. My layout has 1x4s going across the layout as an L-girder. This style allows me to put wire thrugh the foam w/o going through wood.
Ihave always used lightweight joint compound, I have never had any issues with expansion or cracking.