This is an update to that other popular circuit that actually straight up fixed all the issues I was having with the other one and demonstrates functionality reasonably well.
Charging via the panel gets the capacitor to a voltage where it can be used by the boost converter. The boost converter takes the approximately 0.6V source and boosts it to 1.8 - 2V.
This 2V is regulated down by a linear regulator to 1.5V for clean power, but you can definitely see periods where the system cannot supply enough steady-state power to continue, so it lets the output discharge to catch its breath.