How long can I safely use a chain for? My chain is well over the 0.75% extension at which I would normally replace it. 
 However, the cassette and chainrings are also old enough that a new chain would slip on them, so they would also need to be replaced.

The drivetrain currently works, despite being worn, so there doesn't seem much point in replacing anything yet.

How long should I leave it before replacing the entire drivetrain?
The problem with worn, stretched chains are: increased wear on the cassette sprockets and chainrings, poor shifting, chain slipping on the sprockets, reduced efficiency and increased chance of the chain snapping.

Normally it's considered 'safe' to run a chain up to 0.75% elongation before risking encountering those problems. If you really care about sprocket and chainring wear replace at 0.5% elongation.

If the sprockets and rings are already well worn and everything seems to be working OK for you, just keep going until problems really start to manifest or something fails terminally, at which point you replace the cassette, rings and chain in one go.

Chain slip or the chain snapping could of course put you in actual danger of a crash, especially as both are likely to happen when you are applying maximum force on the chain in a low gear ratio.