Dear apoc,
Just to make sure we're talking about the same thing:
Are you saying your new iPad doesn’t charge at all when it's plugged in and on or just that it charges much more slowly, so it won't reach a full charge overnight?
If the latter, that'd be consistent with my tests-- I'd expect a full charge with the unit on would take circa 12 hours.
If it's not charging at all, I think something's off. Do you have another charger you can try? Just in case one is putting out low wattage. Also, do you have all power-hungry services (4G, Bluetooth, Wifi, max screen brightness) engaged at the same time? Maybe you can turn some of them down/off.
Also, here's a thought for a work-around-- I assume you've got your preferences set to never sleep the iPad when you're watching movies, which is why you wake up with a not-fully-charged unit. Try setting it for 15 minute time-out. Even if movie watching doesn’t override that (never tried it), just tapping the screen every so often will keep it awake. After you fall asleep (or the move runs out), it'll put itself to sleep and continue charging normally.
pax / Ctein