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There are more pieces that fit that description, but for the one that would move e1-f4-g6-h8... a 'transparent' intermediate g2 could be slipped in. This would make the trajectory bend left 90 degrees at g2 and then right '45' degree at f4 to continue as Nightrider. Problem is that what is left after e1-g2 would become right after e1-f3, so you would have to split it into left-handed and right-handed chiral moves with the aid of an initial hl or hr. This would then give ChlmpalyfrNhrmparyflN , where the y causes range toggle from leaper to slider. (A convention that the meaning of l and r should be swapped on oblique atoms (or effectively oblique sequences of orthogonal/diagonal legs after the first s modifier) when the move starts left-handed would allow us to shrink that to CmparyflN . But the diagram does not implement that.)

Problem is that such tricks would not work on irregularly shaped boards, or boards with holes, as the 'transparent' (mp) intermediate might hit a hole. This could be solved by allowing intermediate legs to stray off board through an o modifier, so that true transparance can be specified as mpo.