Re: How to improve the left hand.
Yeah, you almost just have to work your left hand very, very, very hard when you're practicing.
I also recommend trying to do more "everyday" things with your left that you normally do with your right, just to help strengthen it and to give your mind more focus on it.
Your body is only going to be able to do what you ask of it (because it adapts). So, work that left hand very hard, but don't be mean to it.