To avoid direct 3D attacks from long-range pieces at first move, instead of introducing passive or new active pawns (which may complicate the game uselessly), I propose to force long-range Pieces to do at least one "normal" move before doing an extra 3D-like move.
I'll probably introduce this as a new variant in the future.
You can have a feeling of what it brings looking at the reduction game of "Mapped Chess" to one board called "3to2"
I recall the main interest of "Mapped Chess": the overall relative forces of Pieces are very similar to the ones in standard Chess game, but adding 3D effects. This would bring a wealth of new situations, and new strategies.