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Another way to project more force is multi-move designs. But they are
tricky, both hard to balance and in need of certain constraints. Yet there
are many interesting things you can do with multiple moves. One possibility
is to allow one piece to make 2 moves or two pieces 1 move each, so that,
for example, some shatranj variant with slow pieces could move 1 of them
twice in a turn. [Yes, David, I decided to take your bait hook, line and
sinker.] Would this make shatranj more strategic? Certainly, there are
vast differences among one piece moving 6 squares, two moving 3 each, or
six pieces moving only 1 square each. But consider some of the recent 2
and 3 square ranged pieces; if they could make 2 consecutive moves, how
quickly could a game end? That easily fits Abdul-Rahman's criterion:
'especially if one mistake can lead immediately to a mate in 1.' 

Gotta continue this later, apparently we're getting a blackout. But I
suggest a few trial games of shatranj with 2 moves might be interesting.