high capacity joule thief/dc-dc converter

I'm trying to make a dc-dc converter with the following characteristics:
Output = 5V regulated at up to 30mA = 150mW
Input 1V (or lower) from a slightly flat AAA.
Assuming a pessimistic circuit efficiency of 50%, then the input current would need to be 150mW / 0.5 / 1v =  300mA which I think a AAA is capable of supplying.
I'm using a variation of "led torch circuit 2" from http://www.talkingelectronics.com/projects/LEDTorchCircuits/LEDTorchCircuits-P1.html, but I've replaced with the 1n4148 with a schottky diode and replaced the 2 LEDs and 29R resistor with a 5k6 and 1k resistor respectively; this should limit the output of the circuit to just under 5v.
I have a 150R resistor to provide a 30mA load to the circuit.

When the input is 2.4V, the output is 4.62V which is close enough to 5v for me. 
But if I decrease the input voltage to 1.14V, then the output voltage falls to 2.7V which is not enough.

I have tried half a dozen hand wound transformers with various turns ratios, wire thicknesses and shapes (slug and toroid) but am unable to achieve 5v out (at 30mA) from 1v in.
Does anyone have any suggestions as to what to adjust, or perhaps a better circuit?

GrotBox (author) 4 years ago
Thanks for you thoughts everyone.
I've actually found/developed a suitable circuit now.
Your asking for too much out of a simple joule thief and a dying 1.5V battery.