What popped in my head was the control module from just about ANY oil or gas fired furnace.
You would have the shut down delay component, thermal sensor and an optic / IR sensor based fail safe ( you could aim the eye at the 4-400's ). Most even have line level relays right on the PC board.
The low fuel sw. in the example below could be coupled to whatever beverage & container you have in the shack to prevent dehydration while strapping...
But seriously, I like your idea and I have a file drawer full of used modules. If you can't find a used or cheap one let me know. Any self respecting burner service guy has them stashed all over the place
D