Yep, you have confirmed what I have just learned. The cap on the output can provide enough juice to charge the sample cap in the micro.
Been playing with the values of the cap and the bleed resistor to fine tune it to the response I'm looking for. I do want to check out the full wave version of the circuit Eric posted, because I believe that it will allow me to achieve a faster response by bumping the peak twice as fast, allowing me to use a faster decay. Once I figure that out, I guess all that's left is to breadboard a quick circuit to validate with real world inputs and then layout and build the pcb.
Best of all, I can see a clear path forward on my project, and for that I owe you guys. Clearly a debt I likely won't have the skill to repay. Thanks for having the patience to support a highly motivated, and generally ignorant (but getting better), hobbyist.