A couple of things that might help.
1) when you are finishing the turn, ski your hip to the handle
2) when you get there, LEAN away from the boat...all the way through the wakes
3) you appear to have your arms bent when you are "pulling". You have to get your arms straight, hands down by your waist...hips forward. This allows for a lot more lean, this will make crossing the wake much easier
Try to feel the movements, or body position that creates speed through the wakes. Take a look at your body position as you pull out to start your gate. You are in a much more stacked position than
when you cross the wakes.
When you finish the turn, you start to lean, then you give up on it and hit the wake with a flat ski. You need to increase your lean as you approach the wake. I know that it seems counter to your survival, but it is way easier and safer to cross the wake on a deep edge.