I would use a Teensy. It has a good audio processing library.
The 65-1200 filter is easy.
The sustain is a bit more complex. I initially thought you would need to record the note and play back the recording but your diagram shows that won't work. I think you can do that effect with companding. The initial loud part of the note should be made softer while the soft part of the note should be made louder. This is a very common filter.
The part you haven't discussed is how to use the output from the Arduino. Are you expecting to plug this into a standard guitar amp? Then the output has to mimic the characteristic of the pickup.