Is the mate-in-n problem of infinite chess with each color using traditional pieces plus one huygens decidable?
Presburger arithmetic with a predicate for the primes is probably undecidable, so at least the technique used by your question's link should not easily generalize to allowing a huygens.

For example, although decidability of the special case I'm about to mention

would follow from there being only finitely many positive even integers that

are neither prime gaps nor sums of two distinct primes, I don't see any way of

proving decidability of mate-in-ONE for king+huygens against a smothered king: