Oven light keeps burning out
 

You need to have the voltmeter connected semi-permanently to the oven bulb outlet so you can monitor the voltage when you first turn the oven on and when you open the door. It does not seem like it burns out on a steady state basis, only on turn-on transients, and you will not see them if you have to open the oven door to connect your voltmeter. You need a screw-in outlet and an extension cord so you can monitor the voltage at turn-on. Even better would be an oscilloscope so you can see the actual transient. If you have a loose neutral anywhere in the circuit, you might have a high transient. For instance, if the timer motor is on the other half of the split 240 Volt circuit, the motor inductance will have a varying impedance at the time the light turns on, and that could screw up the balance of the circuit if the neutral is loose.