Climb up a long, medium-steep hill. Turn around.

Hands in the drops, fingers loosely wrapped around the handlebars and just sitting, relaxed, on the levers. (Very important to be in the drops. I get the anxiety you describe if on the hoods.)

Pedals level (gives you much more stability).

Yes, bum back.

Glide down effortlessly, smile like a madwoman.

Say: "Weeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee!"

Yes, relaxing is key. But you should only relax if you've got good technique, especially the smiling part.