I have a copy of the Ernest Jones book Swing the Clubhead, which was originally called Swinging into Golf when it came out in 1937. The book was an attempt to teach players how to swing like the classic players did, albeit while using steel-shafted clubs.
There's an interesting sequence of pictures in the book that shows Leo Diegel hitting balls while standing on only one foot. The pictures are very small and dark in the book, and I haven't been able to find copies of them on the web, but the concept is an interesting way to learn how to swing.
No doubt you've heard of the famous Jones teaching aid -- a pocket knife attached to a handkerchief. You can read a good explanation of how that works at this GolfWorx page. But the Diegel exercise might help you understand that handkerchief drill better than the drill alone will, so let me explain what Diegel did.
Diegel was right-handed, so Diegel swung while standing on his right foot (his trail foot). So you righties would stand on your right foot, while you lefties would stand on your left foot. The idea is to make a full swing, hit the ball solidly, and finish in a balanced position without your lead foot ever touching the ground. If you overuse your body, you won't be able to keep your balance and will have to put your lead foot down.
Start by hitting pitches and half-shots, then lengthen your swing as you get more confident. This will help you get your hands, arms and body in sync throughout your swing. And when you go back to your normal stance, you should be able to hit the ball longer and perhaps more accurately.
Jones says that Diegel was able to shoot in the low-70s playing this way. I assume he shot some practice rounds this way, in order to work on his rhythm and balance. It sure sounds like a lot more fun than some of the practice techniques I've seen.