Did you just try to draw a connection between a freezer and the temp at which you brumate a tEgu? Good effort, but no way.

You know that the cells in the animals extremities will almost always lose heat and freeze first, and the cells in those areas will then burst during freezing, causing severe pain before the animal is unconscious, correct? You would have to literally flash freeze it to make it humane, and not many people have the means to do that. And dry ice is a bad idea.
Straight Co2 is the best method. All you need is something air tight, even Tupperware with duct tape, a paintball Co2 canister, and some parts to connect them and trigger the release of gas.
Co2 is best right after a vet of course, which is what happened. So it doesn't really matter anyway.