Dry ice is an interesting idea. I want it to work, because it is just so deliciously different.
However, I assume the harsh reality says that it is nearly impossible to suffocate the entire infestation, and more than a few survivors or eggs would remain after the treatment.
The goal isn't to suffocate them, but to draw them into a trap--they're attracted to CO2 because we exhale it. Over time, the hope is you trap and kill the entire population.
I think it'd work for mild infestations, but for larger ones the heat method is really the only option.
However, I assume the harsh reality says that it is nearly impossible to suffocate the entire infestation, and more than a few survivors or eggs would remain after the treatment.