Ideally, you'd get unfit first and then start over. That makes these deep asymmetry issues easier to fix because right now, you have conditioned all sorts of muscles, even ones you don't know about, to get the job done while your body is crooked.
I'd guess that the problem is that you are stronger in your right leg and putting more weight in that stirrup. But! You are are also not strong in your core, hence the riding "scissors style" with your right leg ahead of your left. That's a way to cheat with the problem of maintaining front to back balance.
It's hard (but doable) mental work to change a position that involves proprioception. A physically-hard, mentally easy way? Tie your stirrup leathers to the girth with something breakable. Those bad boys will force you to nix the scissors ride and you'll fix the rest out of pure desperation. Your balance and strength will get corrected. You will get more symmetrical and "honest" with how you use your leg. Carry a whip on the side that is more dull to your leg.
Ask my crooked body how I know. I'm much better now.
ETA: You can fix this riding where ever, whenever and alone. Besides the stirrup thing, you need to ride 60% or more of the time in your bad direction. Do lots of figure eights, comparing the good way to the bad way. Notice any difference you feel in your body *anywhere* while you have what you want in the horse going the good way and focus on recreating that feeling in your body going the other way. This exercise alone will do a great deal of work to increase your body awareness.
I feel your pain, because I tend to do the same. My horses go better left, and I just WANT to be going left all the time. I also have a very strong body that is good at compensating. Lately I have been forcing myself to ride to the right more often than to the left, to reverse this tendency.
One thing I can suggest is to see a good physiotherapist. I went to one for an unrelated issue, but he really helped me to see my crookedness (My body tends to twist left slightly), and designed me some exercises that I could do while looking in a mirror that would help me correct the twist and ride straight (think leg kicks while holding a broomstick so I can see if the stick dips to one side). I need to go back to him for a refresher.
The other thing I would do in the past when I felt crooked was to ride with a crop held across my hands (under my thumbs). When I looked down, I could see that I was riding with my right hand ahead of my left (thanks to aforementioned twist), and was better able to fix it.
"I know nothing with any certainty, but the sight of stars makes me dream." --Vincent Van Gogh