I think it's inevitable that more weight is likely to be placed on one side than the other, depending upon your degree of curvature. I notice it more if I am physically tired and do my best to correct it. I am assuming that if it affects my horse at all, she seems to compensate for it. She moves well from my seat and so, if I was too unbalanced, we would surely be constantly turning off to the right!
That said, I'm not asking for a lot of precision when I'm in the saddle. We only leisure ride and occasionally move cows from A to B, plus I'm only 7st. So I cannot comment as to how it may affect your horse in the disciplines you are training in. Have you discussed this issue with a sports physiotherapist? They may well have more insight into the issue than your average instructor.
I still vote for my pilates machine. I got it as a QVC Today's Special Value, so I could try it out for 30 days and send it back if I couldn't get on with it. All the exercises I do are lying down and the shoulder rests ensure your body is in alignment and you haven't got one shoulder lower than the other. Our house is tiny but it folds away under the bed just fine. Well, I used to put it away, now we've got used to stepping around it. Problem is the dog keeps using the platform as a springboard to get up into the window so he can watch out for the postman!