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if you are willing to open up the question of what kind of piece to call Rabbit it would interestiung to read such cuggestions.
I actually found this page because I was thinking of doing something similar. I think the Rabbit would work best with a combination of Bishop, Knight, and Antelope, because its Betza notation would be BNNY.
After rejecting divergent pieces¹, pieces moving forward/backward as one Bent piece and sideways as another², and pieces making two turns a step apart in the middle³, I thought of retaining the double-bent theme but with both turns at the start. Thus the Rabbit might be defined as making a Mao move followed optionally by a second 45° turn and a Rook move, and the Hare as making a Moa move followed optionally by a second 45° turn and a Bishop move. In each case the second turn could be in either direction. These pieces are both interesting and manageable, and could quickly appear in a variant. There could even be a Contrarabbit and Contrahare with both bends at the end. Of course other CVP members might have even better ideas - including yourself - so if you are willing to open up the question of what kind of piece to call Rabbit it would interestiung to read such cuggestions.
¹ These tend to have servile names, and neither real nor literary lagomorphs are noted for servility. Better suiting divergent pieces involving a Bent or Double-Bent move would be names of the great many dog breeds(although Foxhound and Wolfhound are already taken for Bishop compounds).
² This felt too contrived to me.
³ Still too strong, despite being blockable and barred from moving less than three steps.
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Very Betzan thinking :)
Gilman did end up proposing, a few years later, Rabbit as a Baronwise (i.e. 3D‐exclusive) Chu‐shogi Lion relative; Bunny was tabled later in the same thread for its forward‐only counterpart. They (and the Dukewise — and thus available in Hex — Bull) never made it into Man and Beast though.