Anti-PreChess is a game of placement in which each player places the other player's pieces on the board; another new element is that the placement and movement phases are not separated -- you may move pieces before all pieces have been placed.
Each time it is your turn to move, you may either move one of your pieces that is already on the board, or demand that your opponent place another one of your pieces on the board. Once all your pieces have been placed, the normal rules of chess apply.
All piece placement must be on the owner's first rank, and all Pawn placements must be on the owner's second rank. (In the normal game, there is no Pawn placement.)
If you demand placement when you are in check, the opponent may make any placement which blocks the check.
This applies to all Rooks, of either color, and therefore it is fair to both players -- it doesn't matter what kind of piece you choose, because the decision affects both your pieces and the opponent's.
Kings and Pawns should probably always have their normal moves; in practice, all the pieces should have limited choices -- you get to choose some reasonable move for the piece, you can't say that "Knights move to pink squares and, on odd-numbered Thursdays, they freeze all pieces of Elven extraction".
If you promote a Pawn to a piece that has not yet been placed, you get to decide the rules for that piece -- this is horribly strong, it's true, but on the other hand you are, in effect, becoming the first to put this kind of piece on the board!
This version of the game may be more of an interesting idea than a playable game; on the first move, Black must place a White piece or Pawn, but placing a Pawn either loses or allows W to force an easy draw, while placing any other piece except the King allows the opponent to develop without being obstructed by a Pawn. Although there is still a choice of where to put the K, the fact that the first move is forced even to this extent is a bad sign -- usually this indicates that the game has problems.
While I'm not a good chess player, it strikes me that the "Pie rule" might help this scenario. Player A would place a White piece, then Player B would decide to play White or Black. Or even further, A places a White then two Black, and B decides which Black piece is kept (removing the other), and who plays which color.