There are "UPS" HATs for the RPi Zero that seem to do what we want, but the quality/functionality is all over the place. The better ones don't come with a battery, so expect to spend about $50 for something that doesn't suck (eg the JuiceBox Zero) with a relatively reputable battery (2500mAh) that should allow you to hit your 10 hour target. Granted that depends on how hungry the DAC and the display happen to be.