I had the same exact issue as you, except I couldn't get my spare off when I needed it. I got a flat tire in the parking lot of the tire shop (how ironic lol) and it took me & a buddy 45 min. haggling with the stupid spare tire mechanism and we still couldn't get the damn thing off. I used the lug wrench and followed the instructions provided with the jack and I still couldn't get it off. I almost resorted to using a sawzall and just cutting the damn thing off lol. The folks at GM seriously made the spare tire carrier waayyyy more complicated than it needed to be. I'm quite interested if this method will work, keep us posted!