How does the inclusion of Nightriders lead to a mutual perpetual check?
Betza also believed the crooked bishop to be worth about a rook, but
that's also colorbound, so I suppose it would have the same problem as
BD.
The "aanca" (W>B bent rider) might also be close enough to be an
intersting test, if you want a long-range non-colorbound piece. It's
almost certainly noticeably stronger than a rook, but should still be
closer to rook than queen.
Of course, those both assume your engine can handle nonlinear riders, which
may not be the case...