Hi. As someone who's designed a few audio amps, and taken a keen interest in it, I can tell you this.
Firstly the maximum power is always to be taken with a pinch of salt, so I agree on your maths, use the maximum input to the amp, not the claimed output.
The main thing though, is that actual power of a typical music programme is only about 10% of the maximum possible power (it varies quite a bit according to type of music too). So even if you have the thing cranked up to the point of distortion, I reckon you could get something like 20 hours run time. If you're running it a moderate level, you should be seeing longer runtimes still.
Hope this helps.