Hello, David Cuthbert.
I read your question and I believe I might have a solution for it. Actually, what I have to suggest is not so relevant to your points, but it is all i have!
In my opinion, I think you should check some things on your iPod.
Firstly, try to charge the device for one more hour in advance, after it shows FULLY CHARGED sign.
Then, I think the problem seems to be on the backlight. You should try to follow these instructions:
After it's charged, from the main menu, go to Settings > Playback > Energy Saver. If it's Off, set it to On.
Hit MENU to go back to Settings, then General > Backlight. Set Backlight to 5 seconds (or 2). Go down to Brightness and set it 2 or 3 marks from the bottom (or as low as you're comfortable with).
If you don't change tracks or fiddle with the volume (anything that causes the backlight to turn on), you should get close to the 24 hours; certainly at least 20. If you do change tracks a lot, at least this way the backlight won't consume as much power.
If it's fully charged and you're not getting at least 15-16 hours non-stop playback (without fiddling with it), you should check with Apple and see about getting a replacement.
I found these on another random forum.
You can also check this http://www.apple.com/batteries/ipods.html if the information above does not help you.
Good luck, I hope this was useful.