The tool is called a Hot Knife. Here is a cheap version
that might suit your needs and may be available at a local hobby store and here is a professional model
not available at the local hobby store. If you do decide to use the hot knife to cut the eggcrate be extremely careful and do it in plenty of ventilation like open the garage door and get a cross breeze going. Melting plastic gives off highly toxic fumes which is why it stinks to "high heaven".
It will also kill any canaries in the room too.