With the highest respect for you and your profession I must strongly disagree with your findings.
You made this statement;
Did we start using more acetylene? No. We only added oxygen to the formula.
This is the same in an arcing event. The ionization of the atmosphere around an arc is what causes the heat not more resistance.
The fact that one overcurrent is tripping and the main overcurrent is heating up leads me to believe that something is wired improperly which is causing a high current draw. If the heat was limited to only one overcurrent device I might agree that a lose connection might be the problem as the arcing would only affect the area of the lose connection and not the entire system.
Now back to my original post;
Are both the dryer and stove on the same circuit?