I think one might be able to get around the prime difficulty of the huygens and (weakly) solve Trappist-1 by replacing say all of black's huygens by stronger pieces and all of white's by weaker pieces, each of which are easier to "compute" with. If white can still win (or draw) this, then they can win (or draw) the original. (Is that right?) Doing the reverse would give a similar statement for black (in case the right answer is "draw.")

(2) **Trappist-1** is a type of infinite chess where one of the chess pieces, the huygens, does not obey Presburger arithmetic. Primes cannot be defined using Presburger arithmetic, and therefore the decidability of infinite chess with the huygens is currently unknown: "The huygens piece, however, would break the argument, since the primes are not definable in Presburger arithmetic. So I am not sure whether the mate-in-n problem would still be decidable or not in that case."

Since it isn't even known whether Trappist-1 is decidable, I presume there's no prospect for the game to ever be solved.

I thought you introduced the huygens at least in part specifically to break their argument? Then it's not surprising that it isn't known whether mate-in-n is decidable. And you seem disappointed that the game might never be solved...why?