I think LN2 would be to expencive, it is not too too dangerous but you need a special container, and a supplier. I thought about the dry ice idea and that is a good one, it is cheap and would be easy to put around he outside of the bucket.
Helium is colder yes but even harder to get and harder to make=more expencive.
Dice is the most economical solution, you could also modify an A/c unit to run refrigerant through your wort chiller.
You may end up with frozen wort though with these kinds of systems, not sure if this would adversley affect anything...