Drummers have all their own techniques and ways to improve, usually little things that we grasp easy and fit to our abilities.
When it comes to left hand drumming, my little way or technique, was to basically play lefthanded, or rather open-handed. I forced myself to play everything that I usually play with my right hand, now with my left. You will notice that all of a sudden you have the ability to do more ghost-notes on the snare with more control, because your left hand is filling in on the hihats and ride . . .
Try to play Jazz or 5th note rock beats and try to be creative on the hats with your left hand. It is not easy in the beginning, but pracrice makes perfect. I am actually in the habit now of playing open-hand most of the time.
Another trick is, swop your kit around. In other words, hi-hats and snare on your right hand side and your left foot on the kick pedal. Now you feel just stupid, because your left is doing all the lead work, both with your hands and feet. I found that this little trick has helped me to focus on triplettes and other little nifty grooves on my kick, thus resulting in greater , faster and more complex double bass techniques.
Like I said, it felt real weird for me and it took me a while to adjust my brain-hand co-ordination, but I practiced 3hrs a day like that and even did some gigs like that and now it is almost natural for me.
So pull through and pracrtice hard and use all the tricks and techniques every-one is helping you with to become the drummer you want to be. The RLL RLL RRLL RLL RLL LRR LLRR LLRR RRLLR . . . is a good one to practice with.
O yeah, one last trick. Take your stick in your let hand as normal and hold it between your thumb and you index finger. Using one finger at a time, starting with your middel finger, bounce the tip of the stick on the snare. Start slow and the go faster. Do that with al your fingers and then be creative and try combinations.
So ya, I hoped this helped you, because it helped me.
Very best regards
your fellow drummer