I agree with Slider's the advice to be patient. Cross blocking does not make for good skiing in a course, good skiing in a course makes for cross blocking. There are a few foundational basics you need to have working well to before you will be able to cross block efficiently.
You need to be able to carve a tight enough line so that most of the arc is completed above the gate. This arc of your skis should result in the path of both hips passing inside the base of the gate. Your hands need to be already carried at least chest high with hands and shoulders level (not leaning in). With all these in place, a strong arm with the pole held horizontal should allow you to simply ski thru the gate, catching it just below your glove. There should be no need to swing or punch at it. The outside (blocking) hand should not need to cross the center line of the torso. If you find yourself reaching across for then something basic is missing.
Many racers try to cross block before they are skiing a line to warrent one. Their reaching across their body to block frequently causes upper body rotation and the outside hip moving up and around, flattening their skis and producing a skidded turn. For these racers a clean inside arm clear with an erect upper body and level shoulders can often produce better carved turns that will eventually lead to cross blocking as the line improves. A carved turn with an inside arm clear will beat a skidded cross block every time.
If you can carve the necessary line, one way to start cross blocking is to just set one gate on moderate terrain and ski a line into it from a carving traverse. Keep shoulders level and arms quiet and simply ski thru the gate. Practice from both directions and gradually increase the speed and roundness of your approach arc until you are aproximating your actual race line and can ski thru the gate (hips inside it) with cross blocking and not disturb your carving quality or reaching across your body.
Then set a fixed dimension round turn course with 4 stubby gates leading into a full gate followed by 2 stubbies then 1 full gate, repeating the 2 stubby, 1 full gate sequence. In this drill get you line and turn quality going around the stubbies and focus on skiing the same turn quality thru the cross blocks thru full gates as you can ski around the stubies. Next set 3 stubies, 2 full gates, etc, and then one by one replace the all stubbies with full gates. In this process it is key to keep carving quality high and ski with disiplined quiet hands and upper body. Good Luck!