Have you tried testing how long a set of primary (non-rechargeable) AAA's last? At the current that the 8X and 12X are sucking up, 4.5V may make a significant difference over 3.6V.
In series, it's like a single battery at 800mAh's. (with more voltage)
In parallel, it would be the same voltage as a single battery, with more capacity...
Go with 3 X Energizer e2 lithium primaries and get a lot more capacity...
As Dave mentioned, the driver will not have to use as much current to boost the voltage to what the diode is asking for. Using 3 X e2 lithium primaries will probably be 5 volts on new batteries. (check it out)