DevRickus
The Dirty Jerz
If the ball is in the back of your stance and you are thinning or hitting line drives on short game its usually one of two things. Well it could be many things, but in my experience with THPers its 2 things.
1. Breaking wrists on take away and then when you come back to the ball, its a flip and decel.
2. You know the ball is getting close so you want to try to help it in the air by lifting body up and in case thinning the shot.
For someone with a great sense of speed in putting, it should really be a rather simple move for you assuming you can keep your wrists still.
I fall in to the #2 category but I have been working on it and having some good luck with it. As long as I focus on keeping my head down my body tends to stay there and I hit the ball the way I want.