Key removal

I had the EXACT same problem... You have to replace the shifter... Just go to a salvage yard that has any cobalt parts and see if they have a shifter. If not call around to get a shifter. But you have to replace the whole shifter... I did this and now I can turn the ignition all the way off without having to push in that button.

I had this problem too, on my leased car, so I had to take it to the dealers. There is a recall for this same thing, so maybe your cars would be covered. You are correct that it is an issue with the shifter,though as that is what they replaced.