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Well, this is exactly the kind of games I played. Plus that I do not play
from a single position, but shuffle the pieces in the backrank to have 432
different initial positions. This to minimize the risk that I am putting to
much emphasis on a position that inadvertantly contained hidden tactics,
biasing the score.

If there are such positions, sometimes one side should be favored,
sometimes the other, and the effect will average out. If the posession of
one piece as opposed to another (or a set of others) would systematically
lead to more tactics in favor of that piece even from an opeing position,
I think that is a valid contribution to the piece value of such a piece.

Of course I did all games on a 10x8 board, as I wanted to have piece
values for Capablanca Chess. If I were to do it on 8x8, I would use a
setup like yours, but with Q next to K for both sides, to make the piece
mix to which it is exposed even more natural. (Of course there always is a
problem introducing A and C in 8x8 Chess that they don't fit naturally on
the board, s you have to kick out some other pieces at their expense. But
you don't have to kick out the same pieces all the time. It is perfectly
valid to sometimes give both sides an A on d1/d8, some times a Q, some
times a C, or sometimes Q+C at the expense of a Bishop. The total mix of
pieces in the game should be N AVERAGE close to what it will be in real
games, or you cannot be sure that results are meaningful.

I never went more extreme than giving one side two A and the other two C
(or similarly AA vs QQ and CC vs QQ), by substituting A->C for one side of
the Capablanca array, and C-> for the other. For the total list of
combinations I tried, see:
http://z13.invisionfree.com/Gothic_Chess_Forum/index.php?showtopic=389&st=1
(For clarity: the pieces mentioned in that list where in general the
pieces I deleted from the opening array.)