I think this is one of those "you have to know the rules before you can break them" issues. Really good guys can play with mixed stances or dynamically switch their stances. A couple of excellent players at my club (20+ years of Judo each) do it routinely. I ... don't do that.
Alot of good advice here UK and Ben Know their judo. I would like to throw a curve. In gymnastics they have you step in to a cartwheel and that regularly determines what side you do your gymnastics from. I's possible that you could ba a natural lefty because of your foot work. Guess this dosen't help much as you think you have solved your problem.
Having lefties in a class benefits everyone...makes it easier to train kenka yotsu situations for sure.