Fascinating idea. Since the board starting position never changes, I'd skip the initial table and pivot and just go straight to loading an 8x8 grid with the pieces. I would also make a table of the 6 piece types and movement parameters. So, for ex, the bishop move restriction is dX=dY, the rook (dXdY=0), knight (dXdY=2), etc. Then a child table to record for each piece, the changes in X,Y throughout the game (so the current position of any piece is X = (Xstart + SUM(dX)) & Y = (Ystart + SUM(dY)) and a column to show if the piece was captured. Any proposed "move" (e.g., 3 squares up) would be evaluated against the move restrictions, the current location of the piece and whether or not the move will either land on an empty square, an opponent piece or gulp off the board and either allow or disallow it.
I'm still working on an idea to have a "state" check to know when checkmate happens but that's gonna take a wee bit more time.
But, the idea is very novel and very thought provoking and has provided me with a refreshing distraction from the boring problem I was working on before seeing your post.