In order to fix the short-length problem of the Bishops, make it a billiards board. Getting used to the 3D bounces might be tricky.
To bring it back to 64 squares, cut out the middle square of the 3x3. This looks a lot like the Cylindrical Chess board, but it's different because the Knight can jump over the hole.
Mapping this to the normal board, we get something like: a1 on the middle level, and under b1; b1, c1, d1, top level; e1 under d1; and so on. (I'm far from certain that this is the best mapping).
Using a physical board, I would prefer to stack 8 of the 3x3 doughnuts on top of each other and have the players move up and down. The reason is that it's hard to reach into the middle of a wide 3D board.
You could use a similar trick with a 4x4x8 board, of course; on each 4x4, 8 squares would be missing. Different squares might be missing on different levels! (This would create interesting terrain.)
Rooks, Bishops, and Queens in the lounge would be near the center but would have very limited mobility; Pawns would be unable to advance and promote; Kings might seek deceptive safety here, and Knights would be okay (although even their mobility would be limited).
It seems like the lounge is a place where pieces get some safety in the center, but at the cost of some mobility.
This would work, of course; the only problem would be reaching into the center of the lower board when you needed to make moves there.
You could also extend this idea by adding a submarine board.
You could also cut it back a bit, and have only a few bomber pieces and just a partial board on the upper level. For example,
Cloud-Hopper Chess Above the normal board and pieces, there are 8 floating clouds and 4 Cloud-Hopper pieces (two of each color).
Each move, each player may either make a normal move on the normal board, move a CloudHopper from one cloud to another (possibly capturing an enemy CloudHopper), drop a bomb from a CloudHopper onto an enemy piece directly below (thereby removing that piece from the board), or move an empty cloud (but if you have no more CloudHoppers, you may not move clouds).
Clouds are grey, neither White nor Black, and can be moved by both sides now, except the one that was most recently moved, which is said to have a silver lining (and so it is marked by putting a silver coin on it). One exception: if you move a cloud, move a CloudHopper onto it, and then hey you get offa that cloud, it becomes the little white cloud that cried, and can move again.
Clouds move like Kings, but do not capture each other; and of course only one cloud may be above each square.
Cloudhoppers move like Knights, but only from one cloud to another. CloudHoppers may capture each other.
White's CloudHopper start the game above b1 and g1; Black's Cloudhoppers start above b8 and g8.
Clouds start the game above b1, g1, b8, g8, e4, e5, d4, d5.
The built-in strategic tension is that in an open game, there may not be time to use the CloudHoppers, but in a closed game, they can be very important.
This game is only slightly 3-dimensional, is certain to be a good game and easy for chessplayers to play, and building the extra equipment wouldn't be very hard.
A silly variant: squares under clouds are wet and slippery.