Re: How to improve the left hand.
I'm in the same boat, here's what I'm doing and it's been working well: I went through "Stick Control" and circled all the exercises that have the majority of the strokes played by the left hand. I practice these almost every day and I do it with double bass too. It got to the point after a month or so that I'm making up my own exercises based on ones in that book.
I'm still not quite where I want to be, but I have noticed a significant improvement on my left hand and left foot by doing this.