Different sizes would be good - maybe a "mini game" with 2-3 pieces, or a "mega game" with 5 pieces.
Placing your own pieces is a cool idea - maybe do it "blindly" so you don't know where the opponents pieces are before you start - possible giving you a slight advantage/disadvantage.
Or my favorite idea of all (Same Idea I have for Battleboats!) - play the game on a "hex" type board. Of course on Battleboats, that give you an extra direction to place your piece, in Amazons that would actually take away 2 directions to move a piece.
(hide) If you want to save on bandwidth you can reduce the amount of information that shows up in your pages in the Settings. Try changing the number of games in the main page and the number of messages per page. (pauloaguia) (show all tips)