[beyondCritics]

>However when “few enough” pieces remain on the board (in the endgame), the number of possible game states is small enough that it’s possible to brute force solve the game from each state by enumerating all possible moves and resulting states so as to find the absolute optimal move for any given board position

You can basically never do that, even in the endgame, since you get always exponential blow up! Furthermore with less pieces on the board, they hamper each others movement less, therefore the branching factor really goes down only slightly. If you want to compute all mate-in-n positions, you discover the theoretical values in tiers, by unmoving each tier twice: If you know all mate-in-0,...,mate-in-n positions, unmove the mate-in-n set for the defender and filter out results, where he can avoid moving into the union of the known tiers. Then unmove for the attacker, to find mate-in-(n+1). Repeat until convergence. Repeat the whole process for the left over positions, to find more theoretical values.