Haunted Chess

This Game can be seen as a variation of Ghost Chess (T.R.Dawson) with some additional rules which make it quite different. Here, the distinction is also made between living pieces and spirits, but some relation (see below) is established among them. 
The aim is still to checkmate the enemy King, by livings as well as by spirits.

Setup

The Game needs usual setup, and possibly some markers (coins, elastics, ...) to decide between livings and spirits.

Pieces

The Chessmen sets are also usual ones.

Rules

The same as in orthodox chess, with the additional rules:

1/ Spirits are pieces captured by a living enemy; once released by enemy departure or capture, they may wander around but not capture, unless some living friends “invoke” (summon) them on one of their controlled squares. As soon as the control is lost, the Spirit looses its ability to attack.

2/ Spirits may capture (and annihilate from the game) or threaten living enemies. 
They may not attack enemy spirits directly, but can drive them away by capturing a living piece that just killed an enemy: as two spirits can not share a single haunted place, the one with the highest hierarchical position (-> QRBNP) remains. If equals in hierarchy, the oldest in the place wins.  This rule applies to spirits of the same side as well (when a Spirit attacks an enemy piece which just captured one itself, leaving on the square two Spirit “friends”). 

3/ Spirits can’t cross pieces nor be crossed by any piece: the place is haunted and they “frighten” other pieces. A corollary is that no living piece can threaten a spirit. 

4/ A Spirit pawn may promote to the opposite side only by being “invoked”; it then may reborn to life as a piece of its choice. If it were captured again, it would become Spirit in the chosen piece type. Without being invoked, nothing happens.

Notes

The obvious attacking strategy seems to sacrifice pieces in the enemy King vicinity, place and activate the spirits to capture him.  For the defense, pieces that just captured an enemy should remain as long as possible on the square before leaving a "haunted" place behind.