I found out my project is one of the finalists in the accessible technology Hackaday Prize! I'm super thrilled about this.
I should mention that the current version of the tuner does not use FFT at all. The comments mentioned a beat frequency oscillator and strobe tuner, which is a pretty good description how my tuner actually works.
Meanwhile progress has been a bit slow since university started again. I started to write new software that uses a lower sampling frequency and signed integers so I could filter the input signal to get rid of uninteresting frequencies to make tuning more robust. This does not work at all yet though.
Instead I patched up the current software to run on the new PCB revision, and that still works at least as well as the previous version. When I have the time I intend to write some Labview code to profile my AGC stage, so I can tune its range to be more practical.
As for the problem of the piezzo/humbucker, I decided I should just focus on the piezzo for now, and possibly sell a separate version for electric. That would just be a matter of changing a few resistors.
One thing I'm still considering is using a integrated VCG circuit. I found one that has a 27dB range, which would almost do the trick, but the simulation model is broken, so i don't have faith in designing a circuit with this chip.