I am left handed, but have always shot right handed with pistols and long guns. In addition to being right eye dominant, I shot this way because my Dad and everybody else that shot was right handed and that is the way they knew how to teach. Eventually, shooting guns right handed being natural for me.
I can also shot very well left handed but it is because that is my "strong hand" and it is the one I use every day for almost everything. If you want to be better with your "weak" hand, be it right or left, you have to develop fine and gross motor function with it. It will take awhile but isn't impossible. Think about how a left handed person starts their car every morning.
Start making a concerted effort to do everything from using the remote to opening the pickle jar to turning on light switches to carrying the 50 pound bag of dog food with your left hand and you will begin to pick it up. At the range don't worry so much about how many rounds you fire, just do tons and tons of loading and unloading, presenting the weapon, etc. In fact, use only one or two or three rounds per magazine for quite some time to develop the muscle memory. I think I saw a study that said it takes around 1000 repetitions for something to become natural.
I know this from a lot of personal experience. Back in my younger days, I went through months and months of hardcore handgun training with a lot of talented shooters. I always held my own and usually was in the top 4 or 5 out of 20 or so. When we did disabled drills, weak hand, etc., no one could touch me. Why, because I had 20 plus years of experience using my left hand.