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First, I have to apologize for creating confusion: I mixed up pieces, and
everywhere in my previous posts where I said Llama, I actually meant Alpaca
(Betza WmD). So I have been comparing Alpaca with Guanaco (Betza WmDD). And
it is obvious the Guanaca must be the stronger of the two, as it is fully
upward compatible with the Alpaca. I did not do any tests wit the Llama
(DmW) yet.

[I wll probbaly edit my previous posts to correct this error, soon.]

About the Lion: you are right, I had nearly forgotten about this peculiar
artifact. Now that you reminded me I remember: The Lion seemed to get
stronger by deleting some of its backward moves! But this was only when I
programmed it as a neutrally moving piece, and could be well understood in
this context: if an assymmetric piece moves randomly over the board (i.e.
each move is chosen with equal probbility) it tends to gravitate in the
direction with the most moves. (Actually towards the center of gravity of
its footprint.) So the Lion with fewer backward moves had a net forward
drive, which turned out much more important for its impact on the game than
a few extra means of retreating. (As it already had so many of those.)

But this effect disappeared entirely when I programmed the Lion as a piece
that should be centralized. Then both the nomal Lion (FWADN) and the one
missing a few backward move got much stronger, but the latter was clearly
weaker than the former, as it should. So articacts like this can only have
an impact if the original strategy fr using the piece s far from optimum,
and not very stable (i.e. easily affected by minor issues.)

About the center: Centralization is something different from mobility.
(Although the two happen to correlate in practice.) The reasons why it is
good to centralize pieces are:
1) Pieces like B can attack the opponent's lines in two places, that he
might not be able to simultaneously defend with non-cenralized pieces.
2) Short-range pieces have their worst-case travel time to any place on
the board minimized.
3) Pieces for which (1) or (2) do not apply can attack and defend squares
in the center to chase away or create safe squares for pieces for which it
does.
None of these is related to the number of moves of the pieces per se: a
Wazir only loses moves (and just a sngle one) at the edge of the board, but
it is far better positioned on e4 than on b2. Pawns in the center are
important because of (3). I guess the Guanaco should be centralized also
because of (3), (with only a single forward direction, (1) does not apply,
and because of its rider moves distance (2) plays no role either), which I
initially overlooked.

Btw, it seems we simply were unlucky: where after 100 games the Guanaco
vs. alpaca was only at 48%, after 250 games it had recovered to a 56% lead
for the Guanacos. I will let it run to 400 games (2% statistical error).
Nevertheless, a 6% advantage for two Guanacos over two Alpacas is not very
impressive; it is not even half a Pawn. (I will repeat the test with the
f-pawn deleted for the Guanacos, to get a precise interpolation.) So it
seems the value difference between a single Guanaco and Alpaca is at most a
quarter Pawn.