Abraham Korman explained that the digestive system of rabbits and hyraxes is double. First, the vegetation goes through an initial digestion that breaks down the cellulose. The product is expelled from the body in the form of small pellets, and then they eat them again and put them through full digestion. In practice, this is a process of chewing the cud, except that the product does not return directly to the mouth but is expelled outside and then eaten again (it seems to me that without this process the cellulose cannot be digested).

In the book Watership Down, whose protagonists are rabbits, it is described how they chew what is translated as pellets, and those are apparently these things.

That is true for the rabbit but not for the hyrax.
In any case, this is a very forced answer. I find it hard to believe that if they found a creature that eats its droppings and has split hooves (and in general one could argue that it does not specifically need split hooves, but could instead force some strained interpretation as with chewing the cud), anyone would think it is kosher.

Sorry, the other way around: for the rabbit but not for the hyrax.

I think there are other animals like this too, so that is a problem.
Second, it changes the meaning of chewing the cud a bit.