DC-DC SPMS Boost Converter DCM Prevention
So here is my take, since this application is microcontroller based,
  couldn't one simply just stop the discharge of the inductor when the
  current nears zero?


Think about this - the only way to stop the "discharge current" is to prematurely ground the transistor in the boost device to start "charging" current thru the inductor - you have no option - to keep the inductor open circuit is to enter DCM and that is what you are trying to avoid.

The cycle for a boost converter (or flyback converter) can be: -


Ground the inductor thus current ramps up and inductor stores energy (charge)
Un-ground the inductor  - energy gets released to the output cap and load (discharge)
If inductor can't sustain current into load via diode you enter DCM and basically the inductor becomes open circuit except for the parasitic capacitance of the MOSFET switcher i.e. you get a damped oscillation until...
The cycle begins again.


OK, so then what happens (in that cycle) is a tiny little too much energy becomes transferred to the output capacitor and load (during inductor discharge). This causes the output voltage to rise fractionally higher than what it would and, over a period of a few milli seconds, you might exceed the output voltage that is safe for the load. A few seconds later and you have a dead load and a few seconds later you have a dead boost regulator.

OK before you get to this, the control loop would probably have implemented cycle skipping but cycle skipping is noisier than ordinary DCM so why bother?

BTW, going into DCM isn't that bad - the line regulation of the output isn't as good but it's still quite controllable. There isn't much on the web about this but, due to the self-resonance of the inductor and MOSFET drain capacitance, once DCM is entered there is a small oscillating current in the inductor that is asynchronous to the PWM and when the inductor restarts charging it does so at sometimes a slightly positive or negative current. This can cause the noise on a simple controller such as a fixed-on-period controller.