When I first started working the rope I skipped like a damned lead foot. Now I skipp using my calves alone and my feet barely leaving the ground. I'm not doing crossovers yet because I'm still learning skill with the rope.
For instance, as fatigue builds you might find yourself turning a bit slow evidence by the rope catching the front of your feet and you'll learn to adjust by turning a little faster to maintain a specific rhythm throughout.
Don't worry about speed right now or crossovers. Focus on developing skill, skill, and skill! Never mind who's watching or how you are looking. And above all things...DO NOT GET FRUSTRATED AND PUT THE ROPE DOWN. Keep working at it skipping for 2 - 3 minute rounds and adding on as you get better.
Take it from me. The more you practice, the better you'll get and you'll feel the difference in how you move PERIOD as your balance and coordination will get better. Happy skipping.