For 2-handed solving, you really shouldn't be using your left hand to turn that much; you should use it to grip the bottom-left pieces of the cube so R and U moves are easy to do with your right hand.
I'm slow at it so I was wondering how I could get better with my left hand. I don't like using it and generally don't but I still wanted to ask. My curiosity never sleeps.
I use a bunch of lefty mirrors for some OLL's and PLL's and the only thing that will improve your speed is practicing and drilling the algs. There is no easy way around it. If the dexterity is not there it needs to be learnt and practiced.