Is it safe to discharge Li-Ion to 0V?
Storing them "discharged" to ~3V with the device they were used in
  still preserves lots of energy in the battery.


At 3V a Li-ion battery has almost no capacity left. 

In this graph two 800mAh batteries were discharged at various rates. At 0.1A there was virtually no capacity left at 3.0V. Even at 1A they were 99% discharged.