Single Comment

George, Fergus, your comments are interrelated, so I'll answer them together. 

First, there are [at least] 4 squares that are 3-path. The squares 4 away orthogonally are reached in 2 jumps orthogonally, for 1 path, and in jumping diagonally 'forward' but right or left of the path, the twisted knight moves, you have 2 more paths. If you choose a square 2 away orthogonally, there are the same 3 paths as above in miniature - that is, there are 3 '1-square + 1 square' moves -1 set of wazir moves, and 2 sets of ferz moves. There are also 3 2-square paths. The first is the straight 2-square dabbabah jump. The other 2 paths are alfil then dabbabah jumps. This is 6, but it could be considered only 5, because the 2 wazir steps are over the same squares as the dabbabah jump. As a total technicality, the dabbabah jump doesn't touch the intervening square [it can be occupied], and the 2 wazir moves do, so they are different paths. 

The 'jumping king' can reach 16 squares at a range of 1 or 2, but it can't reach the knight's destination squares in 1 turn. It would need 2 turns to 'make a knight's move'. But the ZigZag General moves twice in a turn, so it can get to knight squares, as long as there is an intermediate empty square to land on during the move. It moves as the jumping king, then may do so again, changing directions. The king, jumping or otherwise, has no chance I can see. The minimum board size for this piece should be 10x10; it should do well on larger boards. 

I suspect the Twisted and fleXible kNights and the ZigZag General are new pieces. But all of them are amazingly powerful. In attempting to tame that power a little bit, I cut the pieces in half, 'literally', and designed Lemurian Shatranj. The Shaman and Hero are half of the Twisted and fleXible kNight. I believe those 2 pieces might also be new.