I worked for years as an upholsterer/ furniture restorer/ part time fisherman and radio controlled aircraft flyer, just two of us.
We cut foam of all sizes with a Russell Hobbs electric carving knife and a 14 inch long thin butchers carving knife, one that was used for slicing cooked meat.
To do what you want to do we would cut all around the block with the electric knife and then reach in to finish cutting with the long knife.
We tried using an hot wire but found it quicker for us using the knives.
If the sun was shining and the mates wife was out working we stopped work and went flying or fishing, great life.