It looks like you're letting go of the handle almost before you even leave the wake. If you don't grab the board and let go with your front hand immediately, you're going to be really stretched out, making it really difficult to land it with that much line tension. Either grab method, nose, etc., or hold on with two hands for the first half of the trick.
Ill second standing up straighter on your cut. This will prevent you from having to cut quite as hard, and will give you more vertical pop with less tension. Make sure your toe 3's are pretty solid too.
As far as landing wrapped being necessary... When I do them, I grab method and I always pass the handle right as I'm landing - I've never landed one wrapped, although many find it easier.