Solitary Patience Chess

the objective of the Game is to replace back the two sets of Pieces (black and white) to their original array from quasi-random initial positions, obeying certain rules close to Card Game Patience.

Setup

Pawns are initially distributed one per file randomly on any rank from 2nd to 6th for white, 7th to 3rd for black. Black Pawns always on the black side relative to White's. Other Pieces are distributed randomly on the board, excepted for their final positions, and with Bishops on different colors.

Pieces

usual set of chess pieces

Rules

1/ Cyclically move Pieces in ascending order (N, B, R, Q, K) by alternating colors (for instance Black B following White N)

2/ Place Pieces in descending order (K, Q, R, B, N) back to the initial array positions when possible. It is not allowed to place one Piece (Q for instance) before all higher order Pieces (K in that case). Once a Piece is placed, it mustn't be moved any more.

3/ When called-Pieces are already placed, you must move one Pawn of the same color one step backward (no further than the 2nd rank for White, resp. 7th for Black) or pass your turn if no Pawn can move.

4/ If any Piece can't be placed anymore (usually because of Pawn blockage), it is allowed to keep on placing lower order Pieces.

5/ When all Pieces that could be placed are in their final position, keep on moving back Pawns alternatively until at least one side is complete (or the most advanced). Then count the number (or the values) of remaining Pieces/Pawns on the Board. The Goal would be to minimize this number (one could also try to complete the arrays within the lowest number of turns).

Notes

1/ Practically, I'm using a Dice to initially place Pieces. First I place White's Pawns from 2nd Rank to 6th, then Blacks, limited by White Pawns, and finally all remaining Pieces by throwing the Dice twice per Piece to get their coordinates. It is preferable to take the origin of White's on Black side and vice versa. You can alternativelly developp a computer program to generate pseudo-random positions subjected to above-mentionned constraints 

2/ Duo Game:
Same rules but the aim for each player is to place first all their Pieces (or count the values remaining when situation is not evolving and the winner owns the min), respecting the alternate play in ascending order, and placement of Pieces in descending order).

3/ This game was reviewed in Variant Chess Magazine Vol7, issue 56  by J.Beasley. He made some constructive comments, one of them being "...I would be incline to replace rules [4 and 5] by the normal patience rule that if you get stuck you loose", and I suppose I quite agree with it.