To the OP, sorry for sidelining your thread. I have now become "that guy" that throws a thread off topic, my bad. Well with close to 100 posts, it was bound to happen. A joke gone wrong, I was not aware this forum was so serious.

Back to the original question.
So I don't have a tire recommendation from my experience. I've taken my Kojaks on grass and my Primo Comets on rough gravel but since they have no tread I would not recommend them because they are very sketchy in sand.

My hardcore MTB friends tend to swear by tire liners over a tire with added protection. Seems to make sense; tire liners are very tough plastic. You might want to give them a try since they are cheaper than a quality tire. I'm not sure if they are made for 20" tires but as long as they are the proper width, you should be able to cut them down to proper length and sand down/feather the edge so it doesn't cut your innertube.

Non folding tires have steel beads to help keep it on the rim, I'm not sure if you can fold a 20" steel beaded tire like you can with the larger tire sizes. A foldable tire has a kevlar bead so you can easily fold up the tire for storage, very helpful if you keep a spare tire on the bike for touring. They are lighter but more expensive.