Two Ring Chess

I make something like The Fellowship of the Ring being symmetric, and then I have some additional ideas and use those too.

Rules

Rules follows of FIDE chess, except as follows:

1. There is a white ring and a black ring, which may be held by any piece of any color.
2. Initially, no pieces have a ring.
3. Whenever a capture is made, if the color of ring of pieces that was captured is not on the board yet, the player whose piece is captured selects one of his unringed pawns to have the ring of his own color. This assignment does not use up a move.
4. If a unringed piece captures a ringed piece, the ring is transferred to the capturing piece.
5. Any piece with its own color of ring can move one space forward or one space diagonally forward (including capture) in addition to its normal movements.
6. Any piece with opponent's ring has the movements of a queen, and loses other powers of movements it may have (i.e. knight moves).
7. No piece with a ring can capture another piece with a ring, and ringed pieces do not give check to a ringed king (except by rule 9).
8. If a unringed piece captures an opponent's non-pawn holding its own ring, the piece of the color of the capturer and of the same kind as captured piece is placed in the space the capturer moved from.
9. Any piece with any ring loses the ability to promote.
10. Pieces with their own ring in their last rank automatically give check, even to ringed kings.
11. Any unringed non-king non-queen piece adjacent to a ringed king or ringed queen, regardless of the color of anything, may steal the ring as a move (for the player owning the thieving piece).
12. Player with no legal moves loses.

Variant 1: Ringed pieces on last rank do not give check to ringed kings.