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Apart from testing Capablanca pieces, I did extensive testing on
short-range pieces, in an attempt to explain their value in terms of their
individual moves. (Alas, I could only do this with Fairy-Max, a minimalist
engine much weaker than Joker80 is in Capablanca Chess). In
particular, I tested handicapped versions of the 'Lion' (FADWN), that
were lacking one or two moves (in left-right symmetric patterns). These
tests confirmed the importance of forwardness: the piece would lose about
twice as much value when you took away some forward moves (like fA) as when
you took away sideway or backward moves (like bA). When I made the piece
divergent, taking away some captures made the total value suffer about
twice as much as when you took away some non-captures.

The importance of forward moves seems a good explanation for the
observation that the R-B difference seems to go down on wider boards. In
cylinder Chess, eqivalent to an infinitely wide board, a Bishop gains about
a full Pawn compared to one that is not allowed to 'wrap around'. The
Rook gains almost nothing (< 25 cP).

I never did any testing of piece values in Knightmate, despite the fact
that I have an engine for it which is much stronger than Fairy-Max (namely
JokerKM). Although most pieces are orthodox there, one could expect
significant value differences with the value of the same piece in FIDE,
because of the different royal piece. (E.g. Rooks no longer have mating
potential; a Queen can force mate wthout royal help.)