Joe, notice that all the theories you have advanced to explain the lack of
a first-turn advantage are general properties of the game, NOT unique to
the opening array. The reversible pieces don't suddenly become
irreversible in the late game; the short-range pieces don't turn into
long-range ones; etc. If those properties were sufficient to prevent a
move from having value, they would prevent ANY move from having value, not
just the first or second one.
But as Muller points out, it seems pretty obvious that you will quickly
lose if you pass ALL of your moves, which means moves must have some value
at some point. IF there truly is no first-turn advantage whatsoever, the
reason needs to be something special about the opening array, NOT the
general properties of the game. The things you cited MIGHT make each move
less valuable, but they cannot possibly reduce the value all the way to
zero.
And while it is conceivable that there is something special about the
opening array that puts the first player in a position of zugzwang, it is
intrinsically unlikely. Most possible positions in most Chess-like games
are NOT instances of zugzwang. And the facts that the opening array
appears to be a "calm" position, and that the pieces are reversible, both
make it substantially LESS likely to be a position of zugzwang--after all,
if my second move can be to reverse my first, and my opponent cannot do
anything to hurt me in the meantime, it is difficult to see how the first
move could have harmed me.
Asking us to verify the non-existence of a first-move advantage by pushing
a few pieces around is silly. Based on this conversation so far, the
first-move advantage in FIDE is barely large enough to be noticed by
masters (it's estimated at approximately one "quantum of advantage").
Perhaps you understand Chieftain Chess as well as a master understands
FIDE, but the rest of us certainly do not. Hypothetically, Chieftain could
have a first-turn advantage that is substantially larger than FIDE and it
would still be all but impossible for us to demonstrate it to you.
We "proved" the existence of a first-turn advantage in FIDE only by
recourse to a statistically-significant sample of high-level games. Unless
you have a similar statistical collection for Chieftain, then none of us
have any real evidence one way or the other, so we are reduced to arguing
generalities--and IN GENERAL it is safe to assume that a randomly-selected
Chess variant has a first-turn advantage.