It's not the same thing but when I took up tennis I'd spend half-an-hour 3 times a week hitting left-handed off a wall with the aim of being able to play with both hands. I metioned it to my coach and he told me that it was okay but that I was probably wasting my time so I stopped. But I've always wanted to be able to play with both hands - versatility is a great weapon on the court (although I must admit my backhand has developed better since).
If it's working for you then there's no reason to change it I guess, but you could put in some time on the court with the intention of trying out hitting groundstrokes and volleys with the right and just experiment. I know Moya is naturally left handed and plays with his right and Nadal the opposite, and I have seen Sharapova hit an occasional groundstroke left handed but I don't know of any one at pro or club level who plays how you do. But there's nothing wrong with being unique.
May I ask, out of interest, if you are right or left handed, and are you happy with your serve, overhead, volley and groundstrokes?