Flyback transformer for hight ratio, low power, DC-DC step-up converter
Here is a design using the LT3757 flyback switcher and it uses a 10:1 transformer to obtain 300 volts from 5 volts. I'm not suggesting you use the chip because it might not work down to 3.6 volts with that transformer but it gives you a starting point with something that is pretty close: -



To open up your options, it might be sensible to get the 300 volts in two stages. Use a regular boost switcher to give (say) 12 volts, then use a flyback (like the 3757). A lot more options will fall into your open hands.