This is how I do them still sometimes. It's kinda the same thing as when you were learning tailwhips, you had to learn to keep the deck under you. You have to keep doing them and keep trying to get your weight over the bars.
The reason people lean back so much on bartwists is because then you don't have to tilt the scooter as much to the side to get the bars around, so it seems a little easier. Just practice tilting the scooter more to get the bars around and keeping your weight over the bars.
Lots of people do this same thing when learning barspins as well, and it's pretty much the same concept.