This version might be easier to remember. If protected bishops, rooks and queens move in the usual way, but only in the forward direction, and the knight moves only in the forward direction. Pawns and kings have the usual movements.
Unprotected pieces then gain their additonal movements. This would certainly force both forces to close with each other.
All thoughts are welcome.

A tactically more dangerous version might use the Amazon for the Queen's promoted state, the Rook and Bishop gain the ability to move as a knight as well and the knight could move 1 or 2 squares forward before moving one diagonally. Pawns move in the usual way.