I wanted to update all the kind people who offered suggestions… thanks!
Lo and behold, the solution to my problems was hiding almost in plain sight: adapters that allow you to mount PM calipers onto a FM fork or rear brake. For now, I am using the black TRP adapters: the FF2 and the FR2, for the front and rear respectively. These adapters even allowed me to stick with my existing rotors!
Where am I going with this???
The major roadblock that I faced to installing a flat bar was this: 4-piston calipers for flat bar levers only come in a PM form factor.
I never knew about the adapters 
.
So far, this is what I got:
Next, I’m installing these Zinn Duro forks:
After that, install a dropper and upgrade the brakes.