Use a li-ion battery at two different voltages
No: you have to treat all cells of a LiIon battery alike, or you will overdischarge or overcharge some cells. Yes, there are &quot;balance&quot; chargers which handle small discrepancies in the capacity or charge level of the different cells, but that's meant to deal with naturally-occurring differences, not deliberate differences in charge or discharge rate.
@Asmyldof is right: you should best use a regulator to convert the full voltage of the battery pack to the 5V needed for your Raspberry Pi. Buck converters can be quite efficient (over 90%); a number of manufacturers sell ICs that only require a few external components.