(a) knights' threats are disconnected and this "flower" approach while good is maybe not ideal. You might as well use a hollow circle at that point.
(b) when we say "chess pieces can be redesigned to be..." then I think about actual physical pieces, it would not do to make these as actual physical pieces because an accidental misplacement turns a rook into a bishop or vice versa. Gotta make the bishop look like it is "sniping" along the diagonals while the rook looks more "sweeping" maybe?
(c) don't make the king a little-queen. Make the king a little square to emphasize "it can only threaten the neighboring square," then it looks more visually distinctive.
The pawns are fun though.