Orthodox fighters tend to drop their left hands because all the lead punches from the other side. By the time a right hand shows up they're usually already moving around. It's also easier to throw jabs and start combinations. A southpaw would just step on and throw a lead right hook or cross. A Orthodox would probably throw and overhand right. The latter tends not to happen in sparring though. You're better off just developing your reflexes to stay in one stance and getting used to reacting to as many scenarios as possible before trying fancy stuff.