Charles Gilman, rather predictably, is way ahead of us here. The helical Rook, Bishop, and Queen are in M&B09 as respectively Proselyte, Brueghel, and Halcyon.
Here is what he says about those pieces:
Crooked odd-move pieces alternate between destinations on two paths of Bent pieces. Names combine the start of the Straight piece and end of the Bent one, where possible alluding to the latter. Square-cell boards have the PROSELYTE, meaning someone changing religion, is a 90° Crooked Panda switching Anchorite paths and the BRUEGEL or BRUEGHEL, a 90° Crooked Bear switching Angel paths and named after a family of Dutch artists. For Proselyte+Bruegel - a Crooked Harlequin switching Gorgon paths, HALCYON as a synonym for kingfisher conveys a Kinglike combining of orthogonal and diagonal.
The Panda is the Slip Rook, which I called a Shifty Rook. A Crooked Panda would make criss-crossing Dabbabbah leaps across a diagonal axis. The Crooked Bear would make criss-crossing Alfil leaps across an orthogonal axis. In contrast to these, the Helical Rook makes a series of criss-crossing Wazir moves, and the Helical Bishop makes a series of criss-crossing Ferz moves. So, I don't think these are the same pieces.
Here is what he says about those pieces:
The Panda is the Slip Rook, which I called a Shifty Rook. A Crooked Panda would make criss-crossing Dabbabbah leaps across a diagonal axis. The Crooked Bear would make criss-crossing Alfil leaps across an orthogonal axis. In contrast to these, the Helical Rook makes a series of criss-crossing Wazir moves, and the Helical Bishop makes a series of criss-crossing Ferz moves. So, I don't think these are the same pieces.