DC Current Booster

What you need is a switch mode regulator. They can reduce voltage with about 80 to 90% efficiency. If you want to know the theoy, look up buck converter.

Bob

 

It would be interesting to investigate using a charge pump to lower the voltage. Charge pumps are normally used to double, triple, etc., a smaller voltage. This approach will not increase current but it will conserve charge, which seems to be your goal. The approach is to use the 5V capacitor to charge another capacitor to 2V through a switch where the switch is controlled by a comparator. The comparator uses a 2V reference to compare the voltage on the 2V capacitor. Of course the comparator and voltage reference would need to be micro-power components to avoid wasting more power than the charge pump is saving, and be capable of operation below 2V in order to get the last bit of charge from the source capacitor.