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interesting idea! i do wonder how the sections would be notated though a number for the section and a number for where that section originally were? number for the section and a new x/y axis for the sections?

You could also have: Wormhole Squares: Pairs of these spaced out over the board - the piece moves out of the Wormhole exactly the same number of squares it needed to move to enter, in the same direction.

Reflective Buffers around the edge - if a piece lands on the square next to one of these, it bounces off the same number of squares in the opposite direction (if a Castle, just goes back, if a Bishop, it bounces at 90°, if a Knight... my brain hurts).

I'm thinking.. A form of dominos? 2 players, each gets a random assortment of tiles with a randomised configuration of pawns and rooks etc., placing them one after the other on the board, 2 pawns beats a knight, pawn and rook beats a queen? hmmm...

On a semi-serious note: would it be better/more interesting/more fun if a turn consisted of (1) *either* moving a piece *or* moving a board section, OR (2) being *required* to do both?

I'd think it'd be more interesting if the answer were no to the first question. I'm not sure on the second. I'd also enforce a timer (30 sec or 1 minute per turn) to keep things moving.

For the second question, you'd also need to consider how pieces traverse it. I think it would be the simplest solution to simply declare the hole to be a completely impassable barrier. That said, it would be more interesting, in my opinion, to consider the edges to be stitched together

I think it would be more interesting/equitable if a tile slide counted as 2 moves. So if you slide a tile you forfeit your next move and the opponent has two consecutive turns.

Not the same thing at all, but this reminds me of the excellent game Sceptre 1027 A.D. Think chess with 9 boards that can be arranged however you like, terrain modifiers for movement (water, forest, castle, etc), and up to 4 players. It's amazing.