A 700x47 is a pretty wide tire. That's equivalent to a 1.9". I'm not certain that switching to one of the other tires is going to do much for you. Deep, loose gravel is going to be a challenge for any tire, as most of the problem is the gravel sliding around under the tire.

It's very unusual for a tire that wide to slip on a level trail. Sounds like poor trail maintenance, piling the gravel too deep.

The Schwalbe looks like a nice tire. I like having a smooth center tread as it makes for a much nicer ride on pavement than knobbies.