Humbucker-style microphone interference cancelling
is it possible to replicate the concept of a Humbucker pickup but with
  microphones instead of guitar pickups?


A humbucker guitar pickup is intended to directly cancel the induced voltage caused by magnetic fields. The magnetic fields that a guitar is susceptible to will be barely a problem for a microphone because the coil is normally much smaller and shrouded by ferromagnetic material that would cause external alternating magnetic fields to bypass the coil.

A guitar pup on the other hand, has an "open" sensitive area in order to project a static magnetic field that can be "modulated" by the movement of the "iron rich" strings. It is much more susceptible to hum because of this.

If a microphone is picking up a lot of hum then, the first question to ask is if the cable feeding the microphone is balanced and is the microphone driving a balanced signal. I suspect that the answer here is no because clearly, an electret is a polarized microphone and one end needs to connect to ground whilst the other end feeds the signal to the amplifier.

I'd try using a conventional moving coil microphone and a balanced cable and balanced input module. A guitar produces an unbalanced signal and the amp is also unbalanced (because it doesn't need to be balanced).

If the magnetic field hum were picked up by the electret - you'd have to use another electret and invert its signal in order to cancel the main microphone's hum but, the problem you have here is that both microphones need to be in close vicinity to "receive" the same level of hum and this means acoustic cancellation and therefore poor levels for the signal you want to keep.