Time triggered switch off
Although you could put this together with one or two monostable multivibrators (which could be implemented with a couple of 555s or a dual multivibrator IC), given your experience it will be much easier, faster, and practical to do it with a micro controller.

A micro controller would take much less space, require fewer components, and would be infinitely more configurable than any analog solution.

An 8-pin microcontroller (AVR/PIC/whatever), or even a 6-pin one, can be programmed to generate any sequence of outputs based on any sequence of inputs. Pulses at different stages, watchdog capability, etc. If it has EEPROM in it, it can even be made to communicate information about the cause of the last shutdown or to monitor different variables in the system. All you need is, power, a decoupling capacitor, perhaps a transistor to control high-voltages, and some simple programming.

Microcontrollers in supervisory roles have been part of computer designs for decades. With the right access and documentation, you might even be able to reprogram one that is already part of the computer to do what you need.