Current booster DC-DC 300mA - 900mA
This is not possible.  You have only 450 mW available, and want to get 450 mW out.  No such current/voltage conversion process (not even a transformer if it were AC) is 100% efficient.

At such low voltages, every possible trick will be required just to get reasonable efficiencies.  You have very little room for any voltage drops on switching elements, resistance of inductors, and diodes.  Synchronous rectification will be essential.  But that's only for reasonable efficiencies.  Again, what you are trying to do is impossible.