Let's invent some very weird pieces

This is worth considering but it has implications. What if we put a Lumberjack and a Time Thief together on a board. Does the Time Thief undo the displacement of pieces when capturing a Lumberjack?

Turning back time should restore the original situation in all its details. You restore normal capture victims. Would you not restore the victim of an e.p. capture, when the TT captures the capturing Pawn? The advantage of this rule interpretation is that it is completely general, and you would not have to make special rules for cases where other weird pieces participate, about which side effects should be undone, and which not.

I don't understand where this idea comes from that castling is a King move. Obviously you move both King and Rook. If capturing a King also restores the Rook to its old location is pretty irrelevant: game over!

I have concluded that you are totally right and adjusted my explanation. It will hardly impact my game against SuperSam1 which is still in the initial phase.

Not if the other Time Thief can still restore the King. I left that part intact, sorry. 

I will do more attempts to find scenarios where the last version of these rules gould give contradictory results.

The FIDE says so. And Superchess players agree upon this when they are playing with the Joker. It must be clear what a Joker can do after castling by the opponent.

I believe in most formal (OTB) tournaments, castling is considered a king move, which can have implications for the touch rule.

When castling the king should normally be moved first. Once a king is moved two spaces, the player is obligated to finish castling by moving the rook.

If a player touches the rook first, then he is indicating that his move will be a rook move, and castling is no longer permitted.

As one may guess, the specific rules can vary by tournament, and they are not always enforced. But when applied, and when enforced, I believe the rules are based on the assumption that castling is indeed a king move.

The touch rule is a separate issue. You cannot allow the player to move the Rook first, because then it is not clear when the move is finished, because the Rook move in castling can also be a legal move for the Rook. For the King you don't have that problem. So it is just a practical consideration. I don't think it has any deeper implication than that. In USCF rules you can still castle if you touch the Rook first, In Chess960 the Rook move should be completed first, and only put the King on its final destination afterwards.

I wouldn't use the Superchess Joker as an example for anything; its rules are completely illogical. It says the Joker doesn't copy any special properties of the moved piece, yet you are ot allowed to move like a Pawn to the 8th rank.

For sure, if two pieces move, we need to make a decision that the move is assigned to only one of the pieces, and the others are just displaced. Because the rules of certain fairy pieces apparently require this.

For the Joker you need to know which piece he can imitate. For the Time Thief you need to know which piece he can capture. For the Magician, you need to know which piece made the move because it should not be an immobilized piece.

Both FIDE and Henk van Haeringen explicitly assign castling to the King, and I will follow that for all pieces that I invent. (This could be very arbitrary, I have no problem with that observation.)

Now that the Joker has been mentioned, a whole lot of extra explanation is needed once we combine the Joker with new pieces. What if I captured a Joker that was imitating a Werewolf, does my piece become a Werewolf?

Does the Angel protect against displacement by the Lumberjack?

What happens if it knocks a pawn to the 1st or 8th rank?

Wouldn't this be a problem then, because this is a contradiction. This might be why castling is considered a king move.

I don't know how UCSF rules solve it when you release the Rook first.

But that there are prescriptions for how the move has to be made (i.e. i what order the pieces have to be touched and released) doesn't mean that it is a move of the piece that has to be touched first.

Interesting issue. Who would decide what it promotes to? If it is the owner, it would mean the player moving the Lumberjack cannot complete the move on his own, but both players would have to decide what it does. Of course you could also delay the promotion until the player owning it would move it, and allow him to decide then. Or you could decide it stays a Pawn forever.

There also is the question whether a Pawn knocked back to 2nd rank again can make a double-step (i.e. if the right to do this depends on virginity or on location). Or a Pawn stepping there from 1st rank. And whether a Pawn on 1st rank has a double, or perhaps even a triple push.

More pieces have displacing abilities. For example the Swapper.

http://www.chessvariants.com/invention/universal-chess

That page doesn't mention what should be done when a pawn ends up on the 1st or last rank after swapping.

Most of all I hope for consistent rules over all displacing pieces. Promotion to a Xiangqi pawn might be an option. That resolves the 2 moves issue and the opponent never has any real advantage from a Xiangqi pawn.

check this out

Simpler options are forced promotion to Queen (or whatever the default promotion choice of the variant), or just keeping it a normal Pawn, but allow in-place promotion of a last-rank Pawn as a separate move.

Or the opponent moving with the Lumberjack can choose the promotion piece and choose the least valuable one.

In general displacing a piece does not generate an immediate advantage. But forcing it to make a weak promotion would be a big advantage. While allowing the opponent to select the piece later, and at the same time move it would basically make the piece an Amazon as long as it is not moved. The most neutral solution would be to allow the opponent to choose the piece later, but require that to consume a turn, so he can use the chosen piece only on the next move. Without being knocked it would have taken a turn to promote the Pawn anyway. I think being forced to make the choice immediately would be too much of a disadvantage, as it would basically give the player that moved the Lumberjack two moves in a row. The only rule addition is then that Pawns on the last rank get the null move as extra move (and because that makes them end on the last rank, they would have to promote), just as on the second rank they get an extra double push. This also doesn't lead to any problem in move notation; if the Pawn gets knockt to e8 you can simply write e8=Q for a later move.

Here is another possible graphic for the Time Thief (I also like the clock). Of course it's also an icon for the grim reaper:

The scythe is used to "reap the dead" and "harvest their souls". Or the time thief uses the scythe to "cut through time."

As far as I know the grim reaper (or death itself) has not shown up on a chessboard yet. It might need to be invented by someone.

I don't suggest it. At least it should have either a bag, a thing to smoke, or a clock.

( I read that book before.)