However, my best guess is that translating the 2D pieces into 3D usually preserves their relative values fairly well.
The existing two-dimensional armies might not benefit equally from moving into the third dimension, but to a large extent they do seem to be okay. Perhaps 3D Grandmasters would notice the difference, but at lower levels of play the values should be close enough: 3D Colorbound Clobberers versus 3D Fabulous FIDEs should be a fair game.
The 3D abstract-translation fbNF is somewhat weaker than the 3D Knight, but the difference is small and this is only one piece in a larger army; meanwhile, the "upright" 3D fbNF is sure to be as strong as the upright 3D Knight.
The 3D WD is quite an interesting piece. Perhaps two of them can checkmate the bare King (with help from their own King, of course).
The 3D HFD is too strong: as White, its first move threatens three different moves that fork or trap multiple enemy Queens.
The other pieces seem to preserve their relative values.
The 3D Colorbound Clobberers and the 3D Forward FIDEs should be okay, and if you use the upright translation, the Nutty Knights should be nice.
The Remarkable Rookies are too strong in 3D, but only because of the HFD. Try using a BD instead.