As a relative beginner myself, I made quite a bit of progress on wake crossings by spending some time forgetting quick turns, and just focusing on the wake crossings. There's a set of YouTube videos that I believe came from a Gordon Rathbun video that break it down into drills that add an additional step with each one. Here's the link to one that focuses on the wake crossings.
Also, having a set of HO blasts as a combo for new folks to learn on, I'd highly recommend finding a different ski. A friend that learned to slalom on the blast said using my old HO freeride felt like a sports car in comparison.