I think the asymmetry in Elk Chess is probably good.
It creates a strategical tension, and castling will tend to be on different wings.
Moreover, should it not be asymetric, then the Elks would tend to be exchanged immediately, e.g., 1.Eg3 Eg6.
Your arguments are plausible and the opinion is to accept.
Notwithstanding I propose you to introduce both types of the Elk
(of course this needs slightly different graphics to distinguish them):
the B/W-Elk: it moves on the black squares as rook, but on the white squares it jumps like a knight
(this is the actual used type); and
the W/B-Elk: it moves on the white squares as rook, and on the black squares it leaps like a knight
(I proposed this type for the white pieces).
With this two types you may build easily different setups (symmetric or not, first move as knight or not).
Did you consider to apply this new method (different move possibilities
depending on the color of the square)
to other combinations of pieces, e.g.
Elk pawns: move (when not capturing) as pawn or as knight (forward only), capture always diagonal;
Notwithstanding I propose you to introduce both types of the Elk
(of course this needs slightly different graphics to distinguish them):
(this is the actual used type); and
(I proposed this type for the white pieces).
With this two types you may build easily different setups (symmetric or not, first move as knight or not).
Did you consider to apply this new method (different move possibilities depending on the color of the square)
to other combinations of pieces, e.g.
Alfred Pfeiffer