Single Comment

I've been playtesting this and I find two flaws:

The Diagonal Bypasser is too weak on a board of this size--since it must
move at least three squares to capture, it has few opportunities.

The Tower of Hanoi is much too powerful. Potentially you can make eight
single stones which equals 8 commoners (non-royal Kings). This is on the
high side of 16 Betza atoms (Queen=5, Amazonrider=8) just considering that
the commoner is the strongest 2-atom piece. Then there must be an unknown
addition for the value of the right to recombine.

The endgame is entirely dominated by the tower.

I've been experimenting with two revisions to address these issues:

The Diagonal Bypasser can capture on any square orthogonally adjectent to
its path, even though the square is also adjacent to the starting or
ending square.  DBb2-d4 can now capture b3, c2, c4, or d3 (but not a2, b1,
d5, or e4). Thius makes it a more useful in the middlegame and fairly
stong in the endgame.

Te Tower's maximum move is reduced to one less than its height: a full
tower can move 7 squares, a three-stone tower can move 2, a one-stone
tower is immobile.  You cannot split off a single stone, but can leave a
single stone behind when splitting. The potential value of the tower is
more like 8 atoms and considerable plus values, still dominating, but its
dominance is much less absolute. Preliminary playtesting indicates that
these two rules make for a more balanced game.

Both Eaglet promotion and The Cube seem quite workable.  Early promotion,
(especially to Mules) is quite easy unless the enemy works to prevent it,
but the opponent can adopt a symmetric strategy and stand pretty well.  

With players who use the cube sparingly (only for a large
material/positional gain or to prevent a large material/positional loss),
The Cube shifts the advantage to Black--making it about the same size as
White's advantage in FIDE, I'd guess. If players use the cube liberally
(to get small gains or prevent small losses), the game is nearer even.

I suspect that a player using the cube sparingly will beat an equally
skilled opponent using the cube more liberally unless the conservative
player's standard's are too high (for example only to give or prevent
immediate mate).