I wish I could upvote this a thousand times. Six years and billions and billions of dollars after launch, League's HUD is still mediocre by 1995 standards. #wtf
You can sort of fix it, though! A couple of patches back they broke the "per-side offset" camera setting, and a Rioter posted a workaround that I've been using ever since...
Switch your camera setting to semi-locked, then press the C key to center/lock the camera on yourself. Now you can use the arrow keys (or nudging the side of the screen) to adjust the camera. When you have it where you want it, press F9, and a little red line will appear around your screen. The red line means the screen no longer slides when the mouse hits the edge. So you can put the camera exactly how you want it, and lock it there.
Is this as good as a real solution, like a contemporary HUD? No, not at all.
Will it allow you to have a whole new wonderful field of vision when you're playing from one of the funny angles? Yes, yes it will.