I am considering building the Hypercube 3D printer with the dual z axis modification.

I am considering building the Hypercube 3D printer with the dual z axis modification. Then I got the idea that if I am going use two steppers for the z axis, why not go all in and use three steppers? This would allow fully automatic leveling of the print bed by having three points of support that can be adjusted by programming offsets to each of the three steppers.

Has this been done before? What firmware would be best for this idea?

You shouldn’t use z motors to correct for levelness skew. That will just misalign the rods and make it more likely for skipped steps. Two are usually used in parallel and on the same stepper driver as well. Best bet is to use a probe and correct by software.

Tbh, a well supported and stiff cantelever bed is fine. There’s no real need for extra support unless you have a 300+ mm Z axis. Look up the FB2020 CoreXY (my design) to see what I mean.