Small DC voltage boost without step-up boost circuit?
300 mA is a lot to ask for in a "minimal components" charge pump circuit.  The driver needs a complimentary pair of transistors rated for at least 1 A.  At 1 kHz, the pump capacitors would be over 300 uF each.  The output would need a linear regulator rated for at least 0.5 A, dissipating over 1 W.  Overall, this seems like a cumbersome workaround to an inductor.