@Schuyler You should not discuss the topic on several threads, because hardly anyone will be able to comprehend this as a problem solution later on.
But to make it clear once again: the EH pin can very well supply an ultra low power MCU such as STM32L. But only if you apply all the necessary power-saving measures and do not connect any power-hungry external devices such as LEDs or your 50mW sensor.
By the way, I consider charging a battery to be a power-hungry application. However, it might be possible to store the harvested energy in a capacitor and then, not simultaneously, use it to supply the STM32L and the 50mW sensor. This is purely a calculation experiment and requires some tricky development.
Good luck
/Peter