With multiply shots per turn, I think it would also fill up the board to quickly. Being able to move like a Knight is an interesting idea which would require a lot more thinking of the possible moves my oppenent has.

Other variant idea's that have been going on in my head:

1) Possible start with 4 "moats" randmly put on the board "moats act like an arrow"

2) Possible let piece "poll vault" over arrows in certain times (for example, if there is more then 5 spaces between piece and 1 arrow, that would be enough running room for the piece to jump the arrow.

3) Possible make "warp" points - maybe from corner to corner, or possible let a player have 1 "random" warp for any peice to any other place on the board (random place on the board)

4) Possible let each player have the possibility to use 2-3 "anti-arrows", which when shot at an arrow will make it disapear.

... again, just some ideas that have been going on in my head