Let's look at it from a diffrent angle.
I've only one episode from the show but from what I can deduce from the OP this guy look like the kind of person to takes his "job" or whatever he is doing very seriously.
So why would he go out of his way to hold his guns/girls in such a retarded manner.
It makes no sense and does not seem consistent with his character design, who is he trying to look cool for?
Like some anon said earlier there is stylish and there is stupid, in the first episode that Arumi-clone (I forget her name) does not swing around that Gorillaz reject (again, can't be bothered) in some unnecessary motions to look cool but she never does anything directly to hamper he combat performance, she for example never stabs herself in the arm and then tries to slash at the monster with her bleadling arm.
But the truth behind why this looks so fucking stupid is that he would looks just as good holding his guns right way up and pointing at his foe, it would be consistent with his design and realistic within the shows universe.
This is also lazy. I mean it does not take to long to come up with a good reason for why he would hold his guns like this. Let's say that Miss .45 in the left has some sort of internal gyro inside her that reacts wheneven she is held upside down that makes he shoot fire instead of lighting, see it's not that hard.
Also is it true that the animation quality drops in the second episode? Because the fights and smooth animation was the only reason I was watching this show.