Is there a safe way to check for a short in a motor (garbage disposal)?
Your equation (Ohm's Law) is correct but you are failing to take into account that the formula you've written is for DC STEADY-STATE conditions.  An INDUCTION MOTOR, which is undoubtedly what you have in your disposal, runs on AC and doesn't follow this limited-case equation.

An induction motor, you can read theory here:

Induction Motor Basics

will look like a low-resistance load at DC.  That, of course, is what you're seeing.  But it's not just a straight wire but rather an inductor so if you apply 60HZ AC to it, you now must account for the DELTA V (i.e. rate of change of the input voltage) to calculate the IMPEDANCE of the load.  Impedance is the actual "resistance" of a complex load to the input power.  Calculating the of an induction motor is fairly complicated since you must include the wiring resistance, the inductance, and as the motor moves, the "back EMF" that it generates.

Long story short: If it blows the circuit breaker when you switch it on, you have a short or other problem in the motor.  If it just hums, you probably have a blocked rotor, and if it doesn't nothing, you may have an open in one of the windings.


  put one of those stupid sideways 20A plugs that nobody uses in the wrong spot


Yes, those ARE used and indicate that this device should be on its own dedicated 20A circuit.  Based on your description, however:


  doing her thing as usual, crammed a bunch of food in the garbage disposal, and ran an extension cord from the plug I installed to a wall outlet. Big surprise, it blew a breaker.


You may have damaged the motor by loading it down and then running it with a poor source of power, specifically the extension cord.

Clear the blockage out of it, see if it has a keyway on the bottom of the unit where you can turn the shaft with a hex wrench, and see if you can get it going again.

If not, time for a new one.  Please either get one that is rated for the power you have or install a proper outlet and circuit for the unit's requirements.