I am trying to build a reed switch based chess board too. The scanning matrix aproach seems the most elegent solution.
However there is another way. (I think, I am new to Arduinio and may have missed something) Have you seen the Centipede Shield? See http://macetech.com/store/index.php?main_page=product_info&products_id=23
. This is a shield with 64 pins that links to the Arduino boad using only a few pins. It also uses ribbon style connectors so that would simplify wiring. I assume you would wire one end of all the reed switches to ground and the other 64 to ribbon ends.
I assume that this would simplify processing as you would just need to scan for a change of state. (Would you still need a resistor or diode on the Reeds?)
If you looked for two move combinations, ie the "From" move followed by the "To" move, then the first move would always be a change of state from closed (Occupied square) to open (Piece gone). The second move would be to an empty square (Open to closed) unless its a capute then its to a closed and you can assume you will get a combination as the old piece is first lifted (closed to open) and the replaced (Open to closed). But all are on the same square and the final state is closed (occupied).
Any practical observations most welcome.