I chose a method; what's done is done now. The method is not great but I didn't seem to have any other reasonable options. I wrapped the egg tightly in plastic to cut off air flow, which increases CO2 fairly rapidly given the small volume. What I had at my disposal was limited. Were it not for the realization that I do actually need to suck it up and analyze things later, I was about ready to deal with it like I do with rodents that don't get a clean death from a trap. Before doing anything, I confirmed that it was totally unresponsive to sound and touch, which at that developmental stage means it was already brain damaged/dead. So things were actually somewhat "better" than I thought in my first post. I don't know exactly how long it takes for the CO2 ratio to get where it needs, but within just a minute or so the repetitive breathing motion had already become less and slower. Obviusly what I chose to do in this situation is not a method I would ever use on a chick that showed any signs of awareness because it is not as fast as other options, but from what I was frantically trying to search on it should be faster than chilling.
In the future I think I need a way to prepare an emergency CO2 bath, which is the only feasible option that I've seen listed for human euthanasia of chickens past day 18 from resesarch facilities and the like (the other methods also use gas but it's not stuff I can make or get). I wish I had something on hand to do that today but I'm out of vinegar, so I couldn't even do the vinegar and baking soda method for making a baloon of CO2. Similarly I have nothing suitable on hand right now to trap CO2/CO from exhaust.