I want to fit a battery backup to a small audio device. Something that
will charge a 7.2 volt Ni-Cad pack without damage no matter how long left
on and run the device at the same time - and switch over automatically if
power fails. Maximum consumption of the device is about 250 mA.
There appear to be 'millions' of supervisory chips out there and I was
hoping someone could recommend one.

It sounds like a maintained emergency light would do what you want