Why does Chopin Etude 10 no 12 not get you what you are asking for??
i am working on a post to link to a technique class that addresses a lot of common issues or questions, heck i downloadd the discussion so i can review it again.in the meantime your are correct there is ample opportunity in the std etudes.for op and others so inclined. This set of studies as variants of chopin op 10 is ignored too much. this ingeniously did what likely others did in practice in some other form or fashion, he swapped the rh and lh a re arrangedi have been on a sort of re done chopin by people other than chipin lately so here it is, been available on std interwebs hiding places a while but you had to know you were looking for it specifically to find easily.
Those just seem to be strict or nearly symmetrical/mirror inversions rather that an actual musical reworking like the Godowsky set, and others I've seen. I do them a lot, but you shouldn't need a written score to do them, in fact you won't get nearly as much benefit from reading them rather than working them out yourself on sight/mentally.Once you get the hang of it, it's actually easier than transposing on sight. It's useful when working on specific passages, but they aren't really worth the time to learn as a whole because they just seem to be almost strict symmetrical inversions.
Finally, most people experience problems with the left hand because they do not have the habit of using it in an integrated, co-ordinated way in their daily lives. Consider the way you cut a steak with knife and fork. Most people (yes, I ask these questions from people Wink) tell me they do it with their hands. But actually they do it with their arms. When it comes to piano playing, beginners will be all right on the right hand since they are using the whole arm in a coordinated way to play. But the left hand is used only form the hand down. Since people are not used to total left side co-ordination, they do not use it when playing the piano.There are two ways of fixing this. First, start to use your left hand - or should I say - the left side a lot in daily life (e.g., when brushing teeth, when opening doors, when washing dishes, when moving stuff - you get the idea). Second get an inverted piano (they are expensive, but they exist!). these pianos are built so that the treble is left and the bass is right. This means that you can play a piece with your left hand playing the treble part and the right hand playing the bass part. The perfect solution, even if you do not hate Bach!