So I powered the edge off completely (or as completely as the power button allows), charged it for a few hours, then turned it back on shortly after 6AM (Eastern). It was showing a full charge at this point. I closed it and left it charge till 2pm. I did use the e-ink to read for about 2 solid hours. When I checked it at 3PM battery status was 89% and again now at 6PM, it shows the battery status at 81%. I have also been keeping it closed when not in use, so I get the "in hibernation" notice on the e-ink screen.

I'm going to check it again in a few hours and I'll let you know what I see then. But for now, I've had 4 hours off the charger with heavy reading use and a 20% drop in battery.

@woodnboats: The usb connection notification is the one you see when you have the usb cable connected. It can't be cleared, but it is supposed to go away when not connected. The power cycle cleared it. There is a possibility that it was keeping a chip or two powered on, but I'm not familiar enough with the device to say that's the case.