Thanks for replying.
The backside of the desk is solid, so I can't screw it down either. The only spot I could screw it down, is on the side of the desk, and in order to get anywhere close to the middle of the desk that way, the arm would have to extend 70+ cm (27 inches), and I've been unable to find such a mount.
There's a few TV mounts that extends that far, but then it has to be wall mounted, which unfortunately also isn't an option. The windowsill frame is made from old wood, and is quite porous.
I never use pivot or swivel, so even if the stand only had height adjustment, I'd be fine with that.