Chess on large boards and especially in higher dimensions might feel more like go 囲碁. There are many battles going on in different parts of the board which only weakly interact because it takes many moves for a piece involved in one battle to move to influence another battle. Perhaps enhance this characteristic by limiting long-range movement to only the movement of the small rook, parallel to orthogonal axes. Another possible enhancement: forbid long-range captures.
Change the scoring to be more like go. There is no king, no checkmate. The game ends with 3 fold repetition or consecutive passes.
For a static final position (consecutive passes) score it by something like territory: maybe the number of squares your pieces can reach before any opponent's piece. If the final position is a loop (repetition) take the average over the loop. Scoring is complicated and best done by computer.
Perhaps the initial position has every square occupied, so there is something to play for, not immediately passing.
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