|Wading room only|
And it's this.
Pictured here in sophisticated blue pen (I usually use crayon) is a circuit diagram which will probably shed some darkness on my plan.
Basically, if I control the 12 volt power supply to the inverter, I can control the pump at the 12 volt level rather than at the 240 volt level, and nobody has to die.
Which is nice.
All I need is a PICAXE 08M chip (owned), a 5 volt voltage regulator to supply 5 volts to the chip from the 12 volt battery (owned - thanks pete), and a float switch. (not owned, but $5 (thanks Nom))
This should actually work.
120 things in 20 years of slapping my head because this solution to Electronics - Low aquaponics water level handling should have been obvious from the start.