I have been trying and failed. Here I have placed a JFET instead of the second NPN, but it doesn't matter, I just can't fork off enough current from the output into the rectifier and smoothing capacitor.
Here are my input wave forms (green) output (blue) and what I get after the rectifier diode (red):
As you can see, there is just not enough juice from the rectifier, and with a lower R3 the output signal is being clipped.
The goal here is to put the output amplitude nicely into the 0-3.3 V range with full swing.
Can it be done? If I need more active components I can just use a MAX9814 and be done with it.
PS: The question was asked if diodes count as active components and let's say for the purpose of this challenge that no, they do not count.
If we have to use a JFET as a variable resistor, we could use the second NPN to amplify the control signal.