Shunts across phases?? Explain what you mean there.
The shunting/dumping happens on the 3 phase side. The R/R detects the ouput voltage on the DC legs, and if the desired output is exceeded, then it causes semiconductors (wired in parallel to the rectifying diodes) between the legs of the 3 phase input to act as resistors, allowing some of the current to flow directly from higher voltage phases to the lower voltage phases (they are neither ground, nor neutral. they are just different phases). This drops the voltage of the waveform being rectified.
Regarding the OP's overheating wires:
The semiconductor (either thyristor or mosfet) doing the shunting generates heat when it acts as a resistor, so R/Rs get hot when the stator is generating more energy than the bike is using. They overheat and blow out when they cannot release enough of that heat to the environment. (Too much current through the resistors, or not enough cooling). Mosfets generate less heat when shunting since they are more 'fast switches' than resistors, so they don't suffer heat-death as easily.
If the R/R is incorrectly sensing too high a voltage, it will effectively drop it's internal resistance to 0, shorting the windings of the stator together, melting the yellow wires, and likely overheats the insulation on the stator windings, leading to a failed/shorted stator.
A R/R can also fail such that a diode can incorrectly pass current in reverse, which is a short between the positive and negative of the battery, melting the DC harness.