That is a cute idea but to benefit from it you'll have to hear better first...
The Pixie receiver gain is just about the gain from the LM386 which is not much.
You know what they say, if you can't hear them you can't work them.

A 5532 dual opamp can replace the LM386.
First stage is a gain/bandpass filter and second stage a gain/lowpass that can drive headphones.
There are numerous examples of this circuit in a QRP kit.
The cost should be around $1 with a little "dead bug" assembly.
The Chinese outfits can probably implement all these mods for $5 shipped... ;