I will soon (after testing) deliver my next (and I hope last) variant of
Cross3D Chess named Cross3D2M. The acronym 2M stands for double move, as
I
got the clue from the new 'Extra move Chess' game by Fergus Duniho.
My main version looked first quite draw-ish, requiring to move 2 sets of
pieces each having relatively half-value compared to a 2D piece, thus
increasing the number of moves and decreasing chances to catch the King.
The Idea to solve this problem is now to allow a double-move for each
player, but restricting it to the same kind of pieces (2 queens for
instance), seeing them effectiveley as a single piece after the second
move. The full strength is recovered, and the number of turns to mate the
King should be reasonable.
A few remarks related to F.Duniho ones, but adapted to this game:
1/ the second move is optional to prevent not suitable stalemate and to
allow single piece move if no other piece of the same kind is available
(moving the same piece is forbiden)
2/ capture is permitted on first and second move, like an hydra would do
(the 2 heads of the 3D-type Queen) ! As the opponent King can't move two
times in a row, and can't call for help from another piece either, he
should't escape checkmate
3/ en passant is allowed on first and second move, because capture is
also
allowed, and double pawn move is also allowed for each move (first and
second) as they can both be captured (should be rare)
4/ the King may be captured by a double check, and the CheckMate advising
will appear on next move  

I hope to improve the game that way, and to appeal to 2D Chess players !