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George, Derek, thanks for your participation. 
George, you bring up the Angel, which you can show 2 different values for,
but this is a highly unusual piece, and one that is not likely to become a
very common piece in variants. As I think we are closer to the beginning
than the end of the evolution of chess pieces [I think we're at the
beginning of the 'great flowering' of chesspieces, analogous to the
explosion of life about, iirc, the beginning of the Cambrian Era, with the
internet acting as free oxygen in the atmosphere.], I think we should let
the pieces evolve around us a bit before we seriously try to incorporate
pieces like that. I think we should stick to very 'chessic' pieces to
begin with - but I could be wrong. However, using David Howe's
'Taxonomy' for an initial ID of piece types would be a start.
Derek, can we actually get that accurate with a generalized formula?
Certainly, FIDE to CRC is very well nailed down. I'm still working
through your paper, but it seems to 'favor' sliders in the analysis a
bit so far, as there are more cases for sliders than leapers, I believe;
quite logically, as you key on sliders, which are *the* piece-type of the
western world. But once you add leaping and side-stepping and a few short
steps instead of 1 longer step, you've injected so much uncertainty that
+/- 5-10% is probably as close as we will get for a long time. We can
avoid the major errors, I think, and value knights as less than rooks, but
will assuredly have trouble [and arguments] over 3 knights vs 2 rooks, and
'if there's a pawn, who gets it?' at higher levels of complexity with
the melange of pieces we are getting.