The difficulty with viewing e.g. the 2.griffin/running ostrich as R2‐then‐B is that the obvious reading of that (in line with the obvious reading of full ‘rook then bishop’ — see also the large shogis' ‘rook‐then‐rook’ and ‘bishop‐then‐bishop’ hook movers) suggests that it could also make the Bishop move after only a single Wazir step, becoming effectively a compound of griffon and ostrich — what Gilman called a Fimbriated griffon (after a kind of outline in heraldry). Which is really quite powerful and not what either of us means afaict.
My view here is that the usual Ostrich (and Osprey) have a move along a given path, but the shortest of its moves is two steps — something it has in common with Tamerlane's picket, Alfonso X's unicorn, and indeed Shatranj's and Xiàng Qí's elephant. For the picket and elephant, the 2‐step move is non‐coprime, and so a one‐step move can be trivially interpolated: for the former this gives the familiar Bishop, while the latter gave a piece that was dubbed the ‘modern’ elephant (and of course with a modern dabbaba to match). For the unicorn it is less trivial (the knight has two possible interpolations) but extending the long‐range move backwards suggests orthogonal‐then‐diagonal over the alternative, giving our Manticore.
In the Osprey's and Ostrich's case, the 2‐step shortest move, as with the picket and elephant, is non‐coprime, and so the obvious interpolation lines up with your 2.bent riders. In the Osprey's case, the alternative exists of doing as with the unicorn and extending backwards, giving a ferz‐then‐bishop‐at‐90°, but fsr 90° turns seem (above‐mentioned hook movers notwithstanding) to be less favoured.
I don't disagree about blockability: what I have termed ‘running’, as opposed to the preëxisting ‘modern’, is explicitly blockable — though arguably calling them ‘lame/stepping modern’ os[prey/triche]s is just as descriptive. Fergus' helical pieces also differ from Charles' Proselyte ⁊c in being (by default) blockable, as well as interpolating.
As for 3‐or‐more.gryphons/manticores, it might indeed be interesting to have names for those (though they might begin to veer into being a little too exotic?), but it'd be equally useful imo to have names for the equally unusual threeleaper‐then‐bishop or quibbler‐then‐rook.
The difficulty with viewing e.g. the 2.griffin/running ostrich as R2‐then‐B is that the obvious reading of that (in line with the obvious reading of full ‘rook then bishop’ — see also the large shogis' ‘rook‐then‐rook’ and ‘bishop‐then‐bishop’ hook movers) suggests that it could also make the Bishop move after only a single Wazir step, becoming effectively a compound of griffon and ostrich — what Gilman called a Fimbriated griffon (after a kind of outline in heraldry). Which is really quite powerful and not what either of us means afaict.
My view here is that the usual Ostrich (and Osprey) have a move along a given path, but the shortest of its moves is two steps — something it has in common with Tamerlane's picket, Alfonso X's unicorn, and indeed Shatranj's and Xiàng Qí's elephant. For the picket and elephant, the 2‐step move is non‐coprime, and so a one‐step move can be trivially interpolated: for the former this gives the familiar Bishop, while the latter gave a piece that was dubbed the ‘modern’ elephant (and of course with a modern dabbaba to match). For the unicorn it is less trivial (the knight has two possible interpolations) but extending the long‐range move backwards suggests orthogonal‐then‐diagonal over the alternative, giving our Manticore.
In the Osprey's and Ostrich's case, the 2‐step shortest move, as with the picket and elephant, is non‐coprime, and so the obvious interpolation lines up with your 2.bent riders. In the Osprey's case, the alternative exists of doing as with the unicorn and extending backwards, giving a ferz‐then‐bishop‐at‐90°, but fsr 90° turns seem (above‐mentioned hook movers notwithstanding) to be less favoured.
I don't disagree about blockability: what I have termed ‘running’, as opposed to the preëxisting ‘modern’, is explicitly blockable — though arguably calling them ‘lame/stepping modern’ os[prey/triche]s is just as descriptive. Fergus' helical pieces also differ from Charles' Proselyte ⁊c in being (by default) blockable, as well as interpolating.
As for 3‐or‐more.gryphons/manticores, it might indeed be interesting to have names for those (though they might begin to veer into being a little too exotic?), but it'd be equally useful imo to have names for the equally unusual threeleaper‐then‐bishop or quibbler‐then‐rook.