It's not a trivial problem. Can you not use 3x C cells instead of 2x D cells, then use an ultra-low quiescent current linear regulator to drop the voltage down to 3.3V?
Failing that, I'd be looking long and hard at ways to make the circuit operate at a lower voltage. What is it that specifically requires 3.3V? Can the circuit not be modified to run at, say, 2.5V instead?