I would like to understand the physics (?) behind that, starting with why ohms law doesn't apply.
The AC motor is the unusual item, not the DC. Most devices tend to be linear, that is, the more drive, the more output. Lamps, resistors, transformers, brushed motors (ac or dc). As you know, there are some items that act in a non-linear, even inverse way. Switch mode power supplies and AC induction motors are both great, everyday examples. SMPS are constant output devices, so when input Volt drops, the input Amps will rise. Very predictably, until the controls run out of headroom. AC induction motors are a close example also. They want to run at a near constant rpm. Not as constant as a true syncronous motor, but almost. If loaded then, you will see it act as a constant power device, trying to keep speed. As the V reduces, the Amps will increase. P=V*I.
In the induction motor, as you then reduce V, I increases and therefore copper loss, which is I*I*R, will rise as a squared function. Thus, the burned out reffer motors at 200V, when designed for 240.
Back to brushed. As V lowers, and load torque is held, the rpm drops and the current also drops. Input power is dropping as a squared function. Winding heat is dropping quickly also, since it is still I*I*R. R is constant. Many a DC motor is speed/power controlled by dropping its supply V, like the vent/ac blower motor in your car.
Back to the OP issue. First off, I don't know what winding temperature is being reached, nor the method and set point of the interrupter. A IR gun would be useful to shoot the armature. It seems to me that the industry needs more/better heatsinking on the motor. Slapping on a truck 24V starter motor is not the best idea. You really want some fins, or other decent method of cooling the armature and rotor. At least a forced air system, or something other than a pile of mass, with little cooling potential.