For sure an schematic (official or reverse-drawn) would be better, but as you know a boost converter should follow an inductive (classical) or capacitive (voltage multiplier) principle, and we could try to guess a rough Thevenin or Norton equivalents of it around a given operating point. If the zener gets too hot, the Voc is too high, and/or the internal resistance is too low. Knowing which is the case, a modification could be devised to the circuit, trying to make it safe.
Regarding the op-amp in this case, it could be part of a not-so-regulated (cheapo) boost converter, or it could be part of the V sensing for protecting the microcontroller. That would deserve analysis after the initial findings. On the other hand, an LM358 can only source a few tens of mA, bellow it's Vcc. That's why if I were MaxFrister, I would start by trying to understand how the circuit behaves and then think whether a mod can be made.