Besides what's on my packing list, what additional stuff should I bring on a deployment to the Middle East?

That depends on if you are riding the FOB life or in a FOB'lit in the middle of nowhere. That is the difference in more socks and baby wipes vs movies and collage classes.

I packed a small hardware kit( hand drill wood screws metal screws bolts lock hasps and extra locks as well as screw drivers with multiple heads even a smaller set for eyeglasses or small items like watches etc. I also packed plenty of repalecement batteries for my flashlights and other electronics