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Since this is a game which involves the goal of a stalemate, the
possibility of a cluttered field is actually desired.  A player would be
wise not to impede their own progress with stone-throwing.

Capturing the opponent's Ariki will be an in-game strategy.  With three
of them, this will be a tough objective to capture them all.  But the
potential is there.  Impeding this piece's moves and stone throws would be a good tactic.

And once a player loses all their Ariki, they might not have the ability
to make their cell goal but they still might capture the opponent Moais. 
Or even to draw the game.

The Mato to’a can only be fully impeded by their own stones or enemy
pieces(not enemy stones).  They cannot be captured.  Send them into the fray.

Remember that the Moais can move swiftly across the field, it is merely
dependent on the connectivity of its stones.

The fact that a computer program has difficulty playing this game does not
negate its potential.  In fact, it increases it.  Once a game has been
fully quantified, although it may have a high degree of difficulty, it
becomes trivial.

For now, this game might best be played between two humans.  Once certain
patterns of play can be discovered, a good computer program might be
worked out.