You could use dry ice, but you would need to stir constantly so you don't get frozen wort around the outside of the dry ice chunks which would insulate them from doing any more cooling. Dry ice is denser than water and wort (SG = 1.400 - 1.600)) and will sink to the bottom of your kettle, which exacerbates the freezing problem. Breaking the dry ice into small pieces would work better than large chunks, but too fine a powder will just make a massive cloud of fog when you dump the dry ice into the kettle, like a Halloween show. It would be a fun experiment to try, but rather pricey.
When using an immersion chiller you need to make sure that either the chiller or the wort are in constant motion. Otherwise you get a boundary layer of cool wort next to the coil that inhibits heat transfer. At that point you are relying on diffusion for heat transfer, which is much less effective than conduction. If you jiggle the coil constantly or stir the wort constantly it will break the boundary layer and you will get much faster cooling because you will be bringing fresh hot wort into contact with the coil all the time. If you have a pump or whirlpool mechanism that is the least tedious way to keep your wort moving. If not, just jiggle the coil up and down and side to side a bit until you are bored, then have someone else take over. You might find that it only takes half the time to cool than if you leave the coil still.