You won't get more Volts times Amps (Watts) out, whatever you do. The only suggestion is to use an inverter to produce 3V @ 600mA, if you already can supply 300mA at 6V. This is for an ideal inverter, with no losses. In reality, with such low voltages involved, I doubt that you'd get more than 60% of what you put in.
This is a case of "If I were you, I wouldn't start from here", I'm afraid. You either need a different set of PV cells or design a different device to use the volts and current that the ones you have can supply.
How have you managed to increase your current from 30mA to 300mA? Was it by going from series to parallel with your PV array? That implies you must have started with a 60V array (??). If this is the case, you may be able to design a more efficient switched mode supply, based on the 60V supply that will give the current output you want - but you still won't get more Watts out than you put in.