I'm pretty sure the housing aka the "pumpkin" is the same for both AT and MT. How ever the actual diff, what is installed inside the housing, is different and the main difference is the final drive ratio. The drive ratio is based on the final drive gear that is installed in the diff. As far as I know you should be able to buy a 3.69 final drive gear and have it installed in your VLSD.
The diff (the "pumpkin") out of my Z. BTW it has a NISMO cover plate hence the cooling fins
Inside of the diff housing for my Z. The red arrow is pointing to the final drive gear. Also the installed diff is a Quaife ATB and the one sitting next to it is the factory VLSD.