Torque RPM Characteristics of Single Phase Induction Motor within Maxwell's Equations
However, due to the AC current in the main winding of the stator, an
oscillating magnetic field is created, which induces an EMF in the
rotor bars, driving a current through the rotor.
My analysis seems to miss out the zero torque near synchronous speed
criterion. What phenomenon is responsible for this which I have not
included?

Although a transformer equivalent circuit is used to analyze induction motors, the EMF induced in the rotor depends on viewing the stator as producing a rotating magnetic field. The rotor emf requires a difference between the rotor speed and the speed of the stator field. Unless the motor is acting as a generator, slip has a value between -1 and +1. It is calculated as s = (n1-n)/n1 where n is the operating speed and n1 is the synchronous speed.
If you look at the equivalent circuit of the motor, you can see that the resistor that models the conversion of electrical energy to mechanical energy has a value of infinity when s = 0. When s = 1, the value of that resistor is zero. At hat point, all of the electrical power received by the motor is lost as heat in the motor. The majority of the heat is dissipated in the physical resistance of the rotor, Rr, a lot of heat is dissipated in the stator resistance, Rs, and the normal amount of iron losses are dissipated.
The torque at zero speed is less than the peak torque mostly due to the voltage drop across Xs and Xr due to the high current drawn by the rotor.
Note that the equivalent circuit below is for one phase of a three-phase motor. A single phase motor is a bit more complicated and essentially requires two such circuits that give you the red and blue curves in your diagram.

Diagram adapted from Malcom Barnes &quot;Practical Variable Speed Drives and Power Electronics&quot;

My question is: within the context of Maxwell's Equations
(physically), how can I calculate these losses using the geometry of
the motor?

That is not really what is needed.