These examples point to thermal time lag as the enemy. While lag is usually unavoidable in a practical process, always be open to ways of reducing it. Switch off does not avoid boil over. Go for the fastest practical sensor. Light gage or even exposed thermocouples.
Optical pyrometers are even faster.
Consider a controller that can throttle back the heater power well ahead of the temperature reaching set point. That is, make the power shrink in proportion to distance from set point. The controller now has a chance to anticipate and head off temperature overshoot and cycling. This action defines it as a proportional controller. Fig 1 shows the elements of such a controller along with its thermocouple and a controlled heater.