Keeping meat safe all day?
In simple terms, meat is safe either at fridge temperatures or cooking temperatures. You cannot leave meat out all day in a switched-off oven, which is essentially room temperature: 2 hours at room temp is the maximum recommended time throughout the meat's lifetime.

Your various suggested methods of cooling involving ice are impractical at best and unsafe at worst. You might keep the inside of the chicken cool if you put ice inside, but what about the outer parts? Also, what would happen to all the water left behind by the ice as it melts?

Seeing as you can't keep the meat at room temperature and you can't practicably keep it cool, I suggest you instead cook it: get a slow cooker (they are very inexpensive), use joints suitable for slow cooking (such as thigh), put it on in the morning, and your chicken will be fall-off-the-bone tender, and safe, when you get back from work.

If you want to have both white and dark meat, joint the chicken (really not that hard - or your butcher could do it), cook the legs/thighs as above, and keep the breasts in the fridge. When you get home, roast the breasts in the oven while you are preparing vegetables or getting changed or whatever, and you have a whole bird cooked and ready to go.