I am not too convinced that a blocking oscillator as a self oscillating boost converter is going to be desperately efficient but the whole thing seems mainly a toy and if you get something all well and good. I suspect that low saturation transistor will be more important than slight changes to the transformer.

The scheme, though simple, does have some problems because the solar panel impedance is high compared to the power out.

A probable solution is to add two small signal transistors and one Schottky Diode, one NPN transistor, its Emitter to ground and Collector and Base connected to the capacitor that goes at the junction of the base feedback winding and the resistor that goes from Positive to the feedback winding junction.

The second to add transistor and the Schottky diode are used to cut off the base drive to the power Transistors at known current to increase the efficiency of the overall circuit.

The 1 ohm resistor has a wrong value, it should be at least 10 to 20 ohms to reduce the switching current of the power transistor.

If there is interest for this modifications, then the cells volts should be increased as much as possible, it would be better to have higher voltage and switching lower current.

the second part to be added if there is interest with a Vin > 6 volts.

They never did answer my QA questions.

Hope your luck is better than mine was.