Is merely using a piece which jumps like a Korean Cannon enough to qualify? Then my own Bifocal Chess has a piece which becomes (by choice) a Korean Cannon or a Korean Vao after each jump.
I am also considering this 12x8 setup:
clrnbqkbnrlc
.pppppppppp.
............
............
............
............
.PPPPPPPPPP.
CLRNBQKBNRLC
wherein C are the same Korean Cannons/Vaos (starting as Cannons, and allowed to capture or jump a Cannon/Vao), L are so-called Leapers whose first diagonal or orthogonal move turns them as a pair for the duration of the game into Cazaux Elephants (AF) or War Machines (DW) (unless one is captured before , turning the surviving Leaper into a Zebra or Camel), and Pawn promotion is allowed only as a Knight, an Elephant, a War Machine, a Camel or a Zebra (one of each per player).