Drywall has an insulating R-value of 0.5. If you are trying to stop heat transfer and thinking about drywall to do that, you are wasting your time (and money). Sure, it will stop the wind from blowing through, but that is about it.
If you are trying to stop heat transfer within the building, you essentially need to look at it as an envelope, but what you are trying to do is build an envelope in an envelope.
My suggestion would be spray foam. Pull out some of the panels in the ceiling to have the contractor spray the foam up in there, or better yet, spray the foam in the upper area. Cover everything because that foam will get everywhere. If you decide to do this, use closed cell foam because it will also be a vapor barrier.
The rest of the suggestions, as well intended as they are, will not work.