low input voltage dc-dc converter
how about the available current ? you didn't mentioned about the current value. to be able to make DC-DC conversion at resonable efficiency you need at least 1A. and the power supply must be made from at least 2 stages. one which can accomodate input voltages between 1.5-6V and will generate 5-10V at 10-25mA, enough to control a boost stage which will be the power stage. i mentioned about the 1.5-6V interval, and not 0.3-6 as you said, since at this voltage is extremely difficult to get some power from the converter. not to mention that the current provided by the cell will be close to zero.
i designed a similar converter which have to produce 12V DC from a single 2V 600Ah battery element.