Mine will count down till1% then die. Then after 5min on the charger bringing up the battery charge indicator will show 18 - 23% charged. The remaining ~80% will take 10 - 12hrs to finish. Is this plausible? Expected? I thought these types of batteries didn't develop memories.
This is not an opinion or guessing as I have been fixed dozen of tablets with similar problem like yours. Battery capacity fluctuation and long charge is an obvious sign of cracked battery connector. I see very often the battery goes up 20 to 40% , depending on the cracks, after resoldering the battery connector. Your problem is very common in many Samsung tablets but I see many users still try to fix something else not related to this connector.
New battery will have the same problem if battery connector doesn't get fixed.
This is an example how the circuit can get fool to read the battery, disconnect your battery then plugin your USB charging cable, press the HOME button, within 10 seconds, you will see the green battery icon show up 100% fully charged, then it will disappear. The charging circuit doesn't see any current coming and it thinks the battery is fully charged. Try it and you will see why the circuit can't read the battery capacity correctly if the connector is cracked.
Here is example of people taking the advice seriously and fixed the problem, threat 17 and 18
http://forum.xda-developers.com/galaxy-note-10-2014/help/battery-fast-drain-t3143951/page2